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

(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.

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.