Answer:
(a) Mrs. Johnson’s class sold 26 cookies, Mr. Smith’s class sold 27 popcorn.
(b) Mrs. Johnson’s class earned [tex]\$65.[/tex] Mr. Smith’s class earned [tex]\$40.5.[/tex] Hence, Mrs. Johnson’s class earned more.
(c) Mrs. Johnson’s class earned [tex]\$24.5[/tex] 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:
[tex]\left\{\begin{array}{l}x+y=53\\ \\2.5x+1.5y=105.5\end{array}\right.[/tex]
Solve it
[tex]\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.,[/tex]
[tex]132.5-2.5y+1.5y=105.5,\\ \\132.5-105.5=2.5y-1.5y,\\ \\y=27,\\ \\x=53-27=26.[/tex]
(b) Mrs. Johnson’s class earned [tex]\$2.50\cdot 26=\$65.[/tex] Mr. Smith’s class earned [tex]\$1.50\cdot 27=\$40.5.[/tex] Hence, Mrs. Johnson’s class earned more.
(c) Mrs. Johnson’s class earned [tex]\$65-\$40.5=\$24.5[/tex] more.
