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3. Mr. Sanchez's class sold fruit pies for $1.55 each and Mr. Kelly's class sold bottles of fruit juice for $1.40
each. Together, the classes sold 60 items and earned $88.20 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:

User Textual
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Answer:

a) Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.

b) Mr. Kelly's class

c) Mr. Kelly's classs earned $1.40 more than Mr. Sanchez's class.

Explanation:

Let x be the number of fruit pies sold and y be the number of bottles of fruit juice sold.

Together, the classes sold 60 items, so

x + y = 60

Mr. Sanchez’s class sold fruit pies for $1.55 each, so x fruit pies cost $1.55x.

Mr. Kelly’s class sold bottles of fruit juice for $1.40 each, so y bottles of fruit juice cost $1.40y.

Together, the classes earned $88.20 for their school, so

1.55x + 1.40y = 88.20.

a) You get the system of two equations:


\left\{\begin{array}{l}x+y=60\\ \\1.55x+1.40y=88.20\end{array}\right.

From the first equation:


x=60-y

Substitute it into the second equation:


1.55(60-y)+1.4y=88.2\\ \\155(60-y)+140y=8,820\\ \\9,300-155y+140y=8,820\\ \\-15y=8,820-9,300\\ \\-15y=-480\\ \\15y=480\\ \\y=32\\ \\x=60-32=28

Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.

b) Mr. Sanchez's calss earned:


\$1.55\cdot 28=\$43.40

Mr. Kellyz's calss earned:


\$1.40\cdot 32=\$44.80

Since
\$44.80>\$43.40, Mr. Kelly's class earned more.

c) Mr. Kelly's classs earned
\$44.80-\$43.40=\$1.40 more than Mr. Sanchez's class.

User Peterxwl
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