Mathematics College

1) Debbie bought 8 oranges and 7 apples for $10.20. Katrina bought 5 oranges and 14 apples for $12.15. How much did one apple and one orange cost?



2) Joel and Janie are selling fruit. Joel sold 2 small boxes of fruit and 5 large boxes for $31. Janie sold 4 small boxes of fruit and 7 large boxes for $47. How much does one small box of fruit and one large box of fruit cost?



3) Carmen is trying to decide which jet ski rental plan to use. Plan A charges a one-time fee of $40 and $25 per hour. Plan B charges a one-time fee of $60 and $15 per hour. After how many hours will the plans cost the same?



4) Julie and Wendi purchased cell phones. Julie’s phone cost $50 and she pays $0.35 per minute. Wendi’s phone cost $70 and she pays $0.15 per minute. After how many minutes of use will Julie’s phone cost more than Wendi’s?



5) 78 students went on a field trip. They went by van or car. The total number of cars and vans were 10. Each car held 5 students and each van held 12 students. How many cars and how many vans went on the field trip?



6) 168 students went on a field trip. They took a total of 10 vans and buses. Each bus held 42 students, and each van held 6 students. How many vans went on the field trip?



7) Christina spent $81.25 on books. Comic books cost $2.25 each and novels cost $7.00 each. If she bought 15 books, how many comic books did she buy?


8) Tina bought 8 pieces of clothing for a total of $164. Jeans cost $22 each and shirts cost $18 each. How many shirts did Tina buy?


9) Farmer Brown had 25 cows and chickens. They had a total of 72 legs. How many cows and how many chickens did Farmer Brown have?




10) Farmer Brown had 28 cows and chickens. They had a total of 96 legs. How many cows and how many chickens did Farmer Brown have?

What you need to do:

Please WRITE both equations for each problem, identify what your variables represent, and solve the system.

I don’t know what to do, so please help me understand by explaining how you got the answer.
I WANT TO LEARN FROM YOU! :)
- Will give BRAINLIEST -


Don’t answer if you are just going to put a link.

Answers

Answer 1
Hey there

Question no.1:

Debbie bought 8 oranges and 7 apples for $10.20. Katrina bought 5 oranges and 14 apples for $12.15. How much did one apple and one orange cost?

Solution:

Let the cost of one apple be "y" and the cost of one orange be "x".

Here,

According to question,

8x + 7y = $10.20 5x + 14y = $12.15

=> 5(8x + 7y) = 10.20 × 5 => 8(5x + 14y) = 12.15*8

=> 40x + 35y = 51 -->(i) => 40x + 112y = 97.2-->(ii)

By Elimination method,

Equation (i) - (ii)

(40x + 35y) - (40x + 112y) = 51 - 97.2

=> 40x + 35y - 40x - 112y = - 46.2

=> - 77y = - 46.2

=> y = 46.2/77

=> y = 0.6

Putting the value of "y" in equation (i) we get,

40x + 35y = 51

=> 40x + 35 × 0.6 = 51

=> 40x + 21 = 51

=> 40x = 51 - 21

=> 40x = 30

=> x = 0.75

Therefore the cost of one orange is $0.75 and the cost of one apple is $ 0.6.

Question no.2:

Joel and Janie are selling fruit. Joel sold 2 small boxes of fruit and 5 large boxes for $31. Janie sold 4 small boxes of fruit and 7 large boxes for $47. How much does one small box of fruit and one large box of fruit cost?

Solution:

Let the cost of a small box be "x" and the cost of a large box be "y".

Here,

According to question,

2x + 5y = $31 4x + 7y = $47

4(2x + 5y) = 31 × 4 2(4x + 7y) = 47 × 2

=> 8x + 20y = 124 ->(i) => 8x + 14y = 94 ->(ii)

By Elimination method,

Equation (i) - (ii)

(8x + 20y) - (8x + 14y) = 124 - 94

=> 8x + 20y - 8x - 14y = 30

=> 6y = 30

=> y = 30/6

=> y = 5

Putting the value of "y" in Equation (ii) we get,

8x + 14y = 94

=> 8x + 14 × 5 = 94

=> 8x + 70 = 94

=> 8x = 94 - 70

=> 8x = 24

=> x = 24/8

=> x = 3

Therefore, the cost of a small box is $3 and the cost of a large box is $5.

Related Questions

12. m is inversely proportional to the square of (p-1) when p=4,m=5.
Find m when p = 6.​

Answers

Jdssbsbsbsbsbssksaaaajaa

In a bag there are six red marbles, four blue marbles, and eigint green marbles. What is the probability that you will draw a green marble? 1. 1/3 2. 4/9 3. 1/18 4. 4/5​

Answers

Answer:4/9 We know, Probability = Favorable Outcome / Total Outcome

Here, Favorable Outcome (Number of Green Marbles) = 8

Total Outcome = 6 + 4 + 8 = 18

P = 8 /18 = 4/9

In short, Your Answer would be 4/9 or 0.44

Hope this helps!

Choose the figure that does NOT belong with the other three figures?

8
11
24
14

Answers

11 does not belong
Remaining three figures are divisible by 2

The 11 figures do NOT belong with the other three figures. Then the correct option is B.

What is a polygon?

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

If all the sides of the polygon are congruent, then the polygon will be known as a regular polygon.

In a trapezoid, the length of all the sides is not congruent. Then the trapezoid (11) figures do NOT belong with the other three figures.

Then the correct option is B.

More about the polygon link is given below.

https://brainly.com/question/17756657

#SPJ2

220,000 population grows 8%. What will population be in 7 years

Answers

Answer:

the population will be 1,540,000 in 7 yrs

Answer: 377041.34

Step-by-step explanation: if it is growing 8 percent then you will add 8 percent to 100 which will equal 108 percent

Plug that into a calculator with the starting number so it wil look like 108% 220,000 and if you do that seven times you will get the answer.

What is the interquartile range of this data 12, 16, 29, 24, 28, 32, 36, 40, 44, 48,
A 6
B 7
C 8
D 9

Answers

Answer: 6

Step-by-step explanation:

I believe it is 6

Taren has a box of 180 pencils. Each time he draws from the box, he replaces it. After 20 draws, Taren selects 8 white pencils, 2 blue pencils, and 10 green pencils.

Which value is an accurate prediction of the number of blue pencils inside Taren's box?

Answers

Answer:

b

Step-by-step explanation:

beacaause I know

Question 2 of 10
If a basketball player missed 33 free throws out of 100, what fraction and
what percentage of free throws did the player make? Choose two answers.

Answers

If a player did miss 33 free throws out of 100, then that would make that fraction a 33/100. Now if we were to make that a percentage, you would have to divide both 33 and 100 which would bring you 0.33 or 33%

AABC is similar to ADEF. The measure of AC = 10, the measure of DE=8, the measure of BC = 6, and the measure of DF = 20.
Find the measures of AB and EF.



Answers

The measure of AB and EF for the similar triangle ABC and DEF are 4 and 12 respectively.

What are similar triangles?

Similar triangles are triangles that have the same shape, but their sizes may vary.

In similar triangles, corresponding sides are always in the same ratio. The angles are congruent.

ΔABC is similar to ΔDEF. Therefore, the sides will form a ratio.

AC / DF = BC / EF = AB/DE

AC = 10

DF = 20

DE = 8

BC = 6

Hence,

10 / 20 = AB / 8

cross multiply

20AB = 80

AB = 80 / 20

AB = 4

Hence,

10 / 20 = 6 / EF

10EF = 120

EF = 120 / 10

EF = 12

learn more on similar triangle here: https://brainly.com/question/11943039

You spent 1/5 of your birthday money on 2 video games.If each video game cost the same amount.what fraction of your birthday money did each video game cost

Answers

Answer: 2/5

Step-by-step explanation: 1/5 divided by 2You do 1/5, then the 2 is a whole number so you have to always put a denominator under a whole number. The denominator will be 1.in this case you will do KCF or KFC  KEEP, CHANGE FLIP.

1/5 you will keep

you will CHANGE the division sign to multiplication, never change when it is multiplication.

1/5 X 1/2

You will FLIP  2/1 into 1/2. Now multiply numerator x numerator, denominator x denominator.

1/5 X 1/2= 2/5

Now you have gotten your answer but for the future, the numerator should never be greater than the denominator, if it is, divide.

Use the example above and determine the fraction of total interest owed. After the fifth month of a 12-month loan: the numerator is: {(n + ) + (n + ) + (n + ) + (n + ) + (n + )} = , and the denominator is: {(n) + (n + 1) + ... + (n + )} = . Therefore, the fraction is numerator/denominator (to the nearest tenth) = %.

Answers

The fraction of total interest owed after the fifth month of a 12-month loan is 64.1%

How to determine the fraction of interest owed?

From the question, we have the following parameters

The numerator is given as:  {(n+11)+(n+10)+(n+9)+(n+8)+(n+7)}The denominator is given as: {(n)+(n+1)+...+(n+11)}

After the fifth month, the equation of the numerator is:

Numerator = (1+11)+(1+10)+(1+9)+(1+8)+(1+7)

Numerator = 50

The equation of the denominator is:

Denominator = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

Denominator = 78

The fraction of total interest is then calculated using:

Fraction = Numerator/Denominator

This gives

Fraction = 50/78

Express as percentage

Fraction = 64.1%

Hence, the fraction of total interest owed after the fifth month of a 12-month loan is 64.1%

Read more about loan and interest at:

https://brainly.com/question/15301789

I WILL GIVE YOU 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

Answer:

39⁰

Step-by-step explanation:

WE KNOW THAT,

SUM OF ALL ANGLES OF A TRIANGLE IS EQUAL TO 180⁰

P+Q+R=180⁰

2x⁰-9⁰+x⁰+33⁰+x⁰=180⁰

4x⁰+24⁰=180⁰

4x=180⁰-24⁰=156⁰

x=39⁰

Subtract the matrices.
What number fills in [?] ?
А
B
2 -9 8
-5 3 2
4 2-1
1 4 -8
-5 -3 7
7 -2 5
4 8 -4
-35-2
A-B =
7 -12 6
3 [?] 7
-12 -1 2
7 3-2

Answers

Answer:

[tex]\sf \bold{\begin{pmatrix}7&-12&6\\ 3&-2&7\\ -12&-1&2\\ 7&3&-2\end{pmatrix}}[/tex]

Explanation:

[tex]\Longrightarrow \ \sf Give n \ A = \sf \bold{\begin{pmatrix}2&-9&8\\ 4&2&-1\\ -5&-3&7\\ 4&8&-4\end{pmatrix}}[/tex]

[tex]\Longrightarrow \ \sf Given \ B = \bold{\begin{pmatrix}-5&3&2\\ 1&4&-8\\ 7&-2&5\\ -3&5&-2\end{pmatrix}}[/tex]

Solve:

[tex]\sf A - B = \begin{pmatrix}2&-9&8\\ \:4&2&-1\\ \:-5&-3&7\\ \:4&8&-4\end{pmatrix}- \begin{pmatrix}-5&3&2\\ 1&4&-8\\ 7&-2&5\\ -3&5&-2\end{pmatrix}[/tex]

subtract the elements in matching positions

[tex]\sf A - B = \begin{pmatrix}2-\left(-5\right)&\left(-9\right)-3&8-2\\ 4-1&2-4&\left(-1\right)-\left(-8\right)\\ \left(-5\right)-7&\left(-3\right)-\left(-2\right)&7-5\\ 4-\left(-3\right)&8-5&\left(-4\right)-\left(-2\right)\end{pmatrix}[/tex]

Final Outcome

[tex]\sf \bold{\begin{pmatrix}7&-12&6\\ 3&-2&7\\ -12&-1&2\\ 7&3&-2\end{pmatrix}}[/tex]

If x = 2 and y = 0, what is the value of xy.​

Answers

Answer:

0

Step-by-step explanation:

xy means x×y

Anything multiplied by 0 is 0.

So 2×0 = 0

Hope this helped and brainliest please.

Find the area of a rectangle that measures 3 1/4 yd long and 2 1/2 yd wide???

Answers

Answer:

Area of rectangle = 65/8 yd²

Step-by-step explanation:

The area of the rectangle is the length multiplied by the width. In this case, we are given the length 3 1/4 yd and the width 2 1/2 yd wide. Therefore,

        ⇒ Area of rectangle = (L × B) = (3 1/4 × 2 1/2) yd²

It is suggested to convert the terms in the expression (3 1/4 × 2 1/2) to improper fraction. Therefore,

        ⇒ Area of rectangle = [(3 × 4) + 1]/4 × [(2 × 2) + 1]/2 yd²

        ⇒ Area of rectangle = [(12) + 1]/4 × [(4) + 1]/2 yd²

        ⇒ Area of rectangle = [13]/4 × [5]/2 yd²

        ⇒ Area of rectangle = 13/4 × 5/2 yd²

Simplify the expression on the right hand side to determine the area.

        ⇒ Area of rectangle = 65/8 yd²

Thus, the area of the rectangle is 65/8 yd².

what is [( 2+ 75.5) - 3] x 2

Answers

Simplify the expression.

149x

hope this is what your looking for

What is the equation of the circle?

Answers

Answer:

○ [tex]\displaystyle (x - 4)^2 + (y + 2)^2 = 25[/tex]

Explanation:

Accourding to one of the circle equations, [tex]\displaystyle (x - h)^2 + (y - k)^2 = r^2,[/tex]the centre of the circle is represented by [tex]\displaystyle (h, k).[/tex]Moreover, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to which term gets which symbol. Another thing you need to know is that the radius will ALWAYS be squared, so no matter how your equation comes about, make sure that the radius is squared. Now, in case you did not know how to define the radius, you can choose between either method:

Pythagorean Theorem

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 4^2 + 3^2 = r^2 \hookrightarrow 16 + 9 = r^2 \hookrightarrow \sqrt{25} = \sqrt{r^2} \\ \\ \boxed{5 = r}[/tex]

Sinse we are dealing with length, we only desire the NON-NEGATIVE root.

Distanse Equation

[tex] \displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = d \\ \\ \sqrt{[-7 + 4]^2 + [-2 - 2]^2} = r \hookrightarrow \sqrt{[-3]^2 + [-4]^2} = r \hookrightarrow \sqrt{9 + 16} = r; \sqrt{25} = r \\ \\ \boxed{5 = r}[/tex]

Sinse we are dealing with distanse, we only desire the NON-NEGATIVE root.

I am joyous to assist you at any time.

how many calories of energy are in 165 g of bananas if there ae 100 c in 110 bananas

Answers

147 calories I looked it up ain’t hard

What is the difference in length between the longest meteor and the shortest meteor? (4 points)

Answers

Answer:

13 / 8 in

Step-by-step explanation:

Longest ( 1 7/8)  - shortest ( 2/8) = 13/8 in

Are 1/2(6x - 2) and 3 - x equivalent?
I really need help!

Answers

No.

1/2(6x-2) =
3x-1

Is not equal to 3-x

Answer:

No

Step-by-step explanation:

So, you can use the distributive property.

1/2(6x)=3x

1/2(-2)=-1

It is 3x-1, not 3-x

PLEASE HELP PLEASE PLEASE HELP

Answers

Answer:

D. Point D

Step-by-step explanation:

4.82 is close to 5 so D is right A and B are not even close. C is a little to close to 4.5 to be 4.82. But D looks like it could be 4.82 to though so D is right.

line h is parallel to line 0; ∠13 = ∠8 use the image of the protractor to find the angle measure of angle 1 then compute all the missing angle measure

Answers

Answer: Below

Step-by-step explanation:

Angles 1, 3, 5, 7 are 120 degrees.

Angles 4, 2, 8, 6 are 60 degrees.

angles 10, 12, 13, 15 are 70 degrees.
Angles 9, 11, 16, 14, are 110 degrees.
angle 17 is 50 degrees.


Find the least common denominator (LCD) 5/12 and 1/2

Answers

Answer:

12 is the lcd

Step-by-step explanation:

because 12x1=12

and 2x6=12

Answer:


12

Step-by-step explanation:

Both 12 and 2 have the factor of 2 in common. (2)(12)/12 gives us the least common LCM (least common multiple) of 12.

Which pair of values are NOT equal?

Answers

Answer:

[tex]\tan \theta ~~ \text{and}~~ \tan( \pi - \theta)[/tex]

Step-by-step explanation:

[tex]\textbf{A)}\\\\-\tan \dfrac{3 \pi}4 = - \tan\left(2 \times \dfrac{\pi}2 - \dfrac{\pi}4 \right) = - \left(- \tan \dfrac{ \pi}4 \right) = \tan \dfrac{\pi}4\\\\\textbf{These pairs are equal.}\\\\\\ \textbf{B)}\\\\\tan \left( \dfrac{5 \pi}4 \right) = \tan \left( 2 \times \dfrac{\pi}2 + \dfrac{\pi}4\right) = \tan \dfrac{\pi}4\\\\\textbf{These pairs are equal.}\\\\ \textbf{C)}\\\\\tan \dfrac{\pi}2= - \tan 90^{\circ} = \infty\\\\\\\textbf{These pairs are equal.}\\\\\\ \textbf{D)}\\\\[/tex]

[tex]\tan ( \pi - \theta ) = - \tan \theta \neq \tan \theta\\\\\textbf{These pairs are not equal.}[/tex]

A pawn show purchase a DVD player for $12.00 and sold it to a customer for 40% more than the purchase price. The customer was charge 7.5% tax when the DVD player was sold. What was the total, including tax?

Answers

Answer:

  $18.06

Step-by-step explanation:

The price the pawn shop charged for the DVD player was 40% more than what it paid, so was ...

  $12.00 + $12.00 × 0.40 = $12.00×(1 +0.40) = $16.80

__

The tax on the purchase is this price multiplied by the tax rate:

  tax = 0.075×$16.80 = $1.26

__

Then the total including tax is ...

  $16.80 +1.26 = $18.06 . . . . . total cost of the DVD player

giving brainliest! 5 (4m +2)

Answers

[tex]5(4m+2)\\\\=20m+10[/tex]

NEED AN ANSWER NOW!!

Answers

Answer:

V = 8.5 cubic units

Step-by-step explanation:

[tex]2\frac{1}{8} =\frac{16+1}{8} =\frac{17}{8}[/tex]

[tex]V=4(\frac{17}{8} )=\frac{68}{8} =\frac{17}{2}= 8.5u^{3}[/tex]

Hope this helps

The functions q and r are defined as follows.
g(x) = -x-2
r (x) = 2x²-1
=
Find the value of r(g(2)).

Answers

g(2)= -2-2
g(2)= -4

r(g(2))= r(-4)
r(-4)= 2(-4)^2 -1
r(-4)= 31
ANSWER=31

Carlos hires a van it costs £120

Answers

Answer:

Step-by-step explanation:

The cost of hiring a car can be worked out using this rule. Cost = £80 + 50p per mile. 50p. = to.s per mile per mile. Carlos hires a car and drives 90 miles.

The growth of bacteria makes it necessary to​ time-date some food products so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product the number of bacteria present is given by f(t)=600e0.1t​, where t is time in days and the value of​ f(t) is in millions. Find the number of bacteria present at each time. ​(a) 2 days ​(b) 3 days ​(c) 1 week

Answers

a) Substitute t = 2 into the formula

= 600e^0.1(2)

= 600e^0.2

= 732.84 million

Therefore, 732.84 million bacteria are present after 2 days

b) Substituting t = 4 days we get

= 600e^0.1(4)

= 600e0.4

= 895.09 million

Hence, 895.09 million bacteria are present after 4 days

c) 2 weeks = 14 days

Substituting t = 14 days we get

= 600e^0.1(14)

= 600e^0.4

= 2433.12 million

Thus, 2433.12 million bacteria are present after 2 weeks

Sara and her friends go to a football game and get snacks from the concessions. She uses various pictures to show what they ordered. Which of the following expressions best represents their order

F. 4d + h + 2f
G. 4d + 2h + 2f
H. h + 2f + 5d
J. 2h + 4f + 3d

Answers

F is the answer :), she ordered 4 drink as you can count, 1 hamburger and 2 fries :)
Your answer would be f
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