Question

Mrs. Johnson’s class sold cookies for $2.50 each and Mr. Smith’s class sold popcorn for $1.50 each. Together, the classes sold 53 items and earned $105.50 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

Answer:

(a) Mrs. Johnson’s class sold 26 cookies,  Mr. Smith’s class sold 27 popcorn.

(b) Mrs. Johnson’s class earned $\ 65.$  Mr. Smith’s class earned $\ 40.5.$ Hence, Mrs. Johnson’s class earned more.

(c) Mrs. Johnson’s class earned $\ 24.5$ more.

Step-by-step explanation:

Let x be the number of cookies Mrs. Johnson’s class sold and y be the number of popcorn Mr. Smith’s class sold.

(a) If Mrs. Johnson’s class sold x cookies for $2.50 each, then they earn $2.50x. If Mr. Smith’s class sold y popcorn for $1.50 each, then they earn $1.50y. In total, $2.50x+$1.50y=$105.50.

Together, the classes sold 53 items, then x+y=53.

You get the system of two equations:

$\left\{\begin{array}{l}x+y=53\\ \\2.5x+1.5y=105.5\end{array}\right.$

Solve it

$\left\{\begin{array}{l}x+y=53\\ \\2.5x+1.5y=105.5\end{array}\right.\Rightarrow \left\{\begin{array}{l}x=53-y\\ \\2.5(53-y)+1.5y=105.5\end{array}\right.,$

$132.5-2.5y+1.5y=105.5,\\ \\132.5-105.5=2.5y-1.5y,\\ \\y=27,\\ \\x=53-27=26.$

(b) Mrs. Johnson’s class earned $\ 2.50\cdot 26=\ 65.$  Mr. Smith’s class earned $\ 1.50\cdot 27=\ 40.5.$ Hence, Mrs. Johnson’s class earned more.

(c) Mrs. Johnson’s class earned $\ 65-\ 40.5=\ 24.5$ more.