Question

100 POINTS!!! Need answer NOW! only correct answers! don't answer if you don't know how to work the problem!!

1.) Mr. Smith’s class sold wrapping paper for $3.50 each and Mr. Davis’ class sold magazines for $2.75 each. Together, the classes sold 72 items and earned $222 for their school.

Write and solve a system of equations that model the problem. Show all your work.

Which class earned more money?
How much more money did that class earn?

Answer 1

Mr. Smith's class earned more money.

They earned $2 more than Mr. Davis' class.

Explanation:

`\text{Let}\\\\x-\text{number of wrapping paper of Mr. Smith's class}\\y-\text{number of magazines of Mr. Davis' class}\\\$3.50x-\text{the amount obtained from the sale of wrapping paper}\\\$2.75y-\text{the amount obtained from the sale of magazines}`

`\bold{SYSTEM\ of\ EQUATIONS:}\\\\\left\{\begin{array}{ccc}x+y=72&\text{subtract}\ y\ \text{from both sides}\\3.5x+2.75y=222\end{array}\right\\\\\left\{\begin{array}{ccc}x=72-y&(1)\\3.5x+2.75y=222&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3.5(72-y)+2.75y=222\qquad\text{use the distributive property}\\\\(3.5)(72)+(3.5)(-y)+2.75y=222\\\\252-3.5y+2.75y=222\qquad\text{substract 252 from both sides}\\\\-3.5y+2.75y=222-252\qquad\text{combine like terms}`

`-0.75y=-30\qquad\text{divide both sides by (-0.75)}\\\\\boxed{y=40}\\\\\text{Put it to (1):}\\\\x=72-40\\\\\boxed{x=32}\\\\\$3.5x=\$3.5\cdot32=\$112\\\\\$2.75\cdot40=\$110\\\\\$112-\$110=\$2`