Mr. sanchez class sold fruit pie's for $1.85 each and mr. kelly sold bottles of fruit juice for $1.25each. together the classes sold 79 items and earned $127.55 for the whole school? a) write and solve a system of equations that model the problem b) which class earned more money? c) how much more money did that class earn?

A] suppose Mr. Sanchez class sold x bottles and Mr. Kelly sold y bottles:
Total number of bottles will be:
x+y=79
If Mr. Sanchez sold each bottle for $1.85 and Mr. Kelly sold each bottle for $1.25, then the total amount will be:
1.85x+1.25y=127.55
Hence the system of equations will be:
x+y=79i
1.85x+1.25y=127.55ii

Solving the equation by substitution we proceed as follows:
from equation i:
x+y=79
⇒x=79-yiii
substituting iii in ii and solving for y we get:
1.85(79-y)+1.25y=127.55
146.15-1.85y+1.25y=127.55
-1.85y+1.25y=127.55-146.15
-0.6y=-18.6
hence:
y=-18.6/-0.6
y=31
therefore:
x=79-31=48
therefore the number of bottles sold by Mr. Sanchez was 48 and that sold by Mr. Kelly was 31.

b] To get which class earned more we first find total amount earned by each class.
Total amount earned by:
i] Mr. Sanchez=48×1.85=$88.8
ii] Mr. Kelly=31×1.25=$38.75
Therefore we conclude that Mr. Sanchez class earned more money than Mr. Kelly's class.

c] To get the difference of the amount earned, we take the difference of the earnings made by the classes:
=88.8-38.75
=$50.05
therefore Mr. Sanchez class earned $50.05 more money than My. Kelly