Question

(Score for Question 3:_ of 16 points)

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:

Answer 1

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.