Question

3. Mr. Sanchez’s class sold fruit pies for $1.45 each and Mr. Kelly’s class sold bottles of fruit juice for $1.25 each. Together, the classes sold 53 items and earned $70.85 for their school.

(a) Write and solve a system of equations that model the problem. Show all your work.
(b) Which class earned more money?
(c) How much more money did that class earn?

Answer 1

Let x be the number of fruit pies sold by Mr. Sanchez's class, and y be the number of bottles of fruit juice sold by Mr. Kelly's class.

(a) We can set up a system of equations to model the problem:

x + y = 53 (total number of items sold)

1.45x + 1.25y = 70.85 (total amount earned)

To solve this system using substitution, we can rearrange the first equation to solve for one variable in terms of the other:

x + y = 53

x = 53 - y

Then substitute x = 53 - y into the second equation:

1.45x + 1.25y = 70.85

1.45(53 - y) + 1.25y = 70.85

76.85 - 1.45y + 1.25y = 70.85

0.2y = 6

y = 30

Substituting y = 30 into the equation x + y = 53 gives:

x + y = 53

x + 30 = 53

x = 23

So Mr. Sanchez's class sold 23 fruit pies and Mr. Kelly's class sold 30 bottles of fruit juice.

(b) To find out which class earned more money, we can calculate the total amount earned by each class:

Mr. Sanchez's class: 1.45 x 23 = $33.35

Mr. Kelly's class: 1.25 x 30 = $37.50

Mr. Kelly's class earned more money.

(c) The amount by which Mr. Kelly's class earned more than Mr. Sanchez's class is:

$37.50 - $33.35 = $4.15