13 pts

3. 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?

S = Sanchez's class, k = Kelly's class

s + k = 79 ... s = 79 - k

1.65s + 1.36k = 118.17

1.65 (79 - k) + 1.36k = 118.17

130.35 - 1.65k + 1.36k = 118.17

-1.65k + 1.36k = 118.17 - 130.35

-0.29k = - 12.18

k = - 12.18 / - 0.29

k = 42 < = = = Kelly's class sold 42 bottles of fruit juice

s + k = 79

s + 42 = 79

s = 79 - 42

s = 37 < = = = Sanchez's class sold 37 fruit pies

(b) Kelly's class earned : 42 (1.36) = 57.12

Sanchez's class earned : 37 (1.65) = 61.05

therefore, Sanchez's class earned more money

(c) Sanchez's class earned (61.05 - 57.12) = $ 3.93 more