Mr. Sanchez's class sold fruit pies for $1.65 each and Mr. Kelly's class sold bottles of fruit juice for $1.36 each. Together, the classes sold 79 items and earned $118.17 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?

Let P represent the number of pies sold and J represent the number of juices sold.

a)

The first equation for the sum of the sales:

P + J = 79

P = 79 - J

Next, for the sum of the amounts earned:

1.65P + 1.36J = 118.17

Substituting P,

1.65 (79 - J) + 1.36J = 118.17

J = 42

Using this value of J,

P = 79 - 42

P = 37

b)

Mr. Sanchez's class earned: 1.65 x 37 = $61.05

Mr. Kelly's class earned: 1.36 x 42 = $57.12

So Mr. Sanchez's class earned more money.

c) Mr. Sanchez's class earned:

61.05 - 57.12

= $3.93 more than Mr. Kelly's class

We let x be the number of fruit pies that Mr. Sanchez's class sold and y be the number of fruit juice that Mr. Kelly's class sold. The total number of items is 79. That is,

x + y = 79

Also, the total amount earned is $118.17. That is,

1.65x + 1.36y = 118.17

Solving for the system of linear equation will give us the values of x and y which are 37 and 42, respectively.

Solving for the amount earned by each classes:

Mr. Sanchez's : 1.65 (37) = $61.05

Mr. Kelly's : 1.36 (42) = $57.12

Thus, Mr. Sanchez's class earned more by $3.93.