Question

Mr. Sanchez’s class sold fruit pies for $1.32 each and Mr. Kelly’s class sold bottles of fruit juice for $1.77 each. Together, the classes sold 90 items and earned $140.40 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)
`1.32x+1.77y=140.40...(1)`

`x+y=90...(2)`

(b) Mr. Kelly's class earned more money.

(c) $29.52.

Explanation:

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

We have been given that Mr. Sanchez’s class sold fruit pies for $1.32 each. So the earnings from selling x fruit pies will be 1.32x.

Mr. Kelly’s class sold bottles of fruit juice for $1.77 each. So the earnings from selling y bottles of fruit juice will be 1.77y.

As total earnings are $140.40 for their school. So we can represent this situation in an equation as:

`1.32x+1.77y=140.40...(1)`

As the classes sold 90 items, so we can represent this situation in an equation as:

`x+y=90...(2)`

Therefore, our required system of equation will be:

`1.32x+1.77y=140.40...(1)`

`x+y=90...(2)`

(b) Let us find the number of fruit pies and juice bottles by using substitution method of solve system of equations.

From equation (2) we will get,

`x=90-y`

Substituting this value in equation (1) we will get,

`1.32(90-y)+1.77y=140.40`

Upon using distributive property
`a(b+c)=a*b+a*c` we will get,

`118.8-1.32y+1.77y=140.40`

`118.8+0.45y=140.40`

`118.8-118.8+0.45y=140.40-118.8`

`0.45y=21.6`

`(0.45y)/(0.45)=(21.6)/(0.45)`

`y=48`

As Mr. Kelly's class sold 48 bottles of fruit juice, so earnings from selling 48 bottles of juice will be:

`\text{Earnings from selling 48 bottles of fruit juice}}=48* 1.77`

`\text{Earnings from selling 48 bottles of fruit juice}}=84.96`

Therefore, earnings of Mr. Kelly's class from selling 48 bottles of juice will be $84.96.

Let us find the number of fruit pies by substituting y=48 in equation (2).

`x+48=90`

`x+48-48=90-48`

`x=42`

As Mr. Sanchez’s class sold 42 fruit pies, so earnings from selling 42 fruit pies be:

`\text{Earnings from selling 42 fruit pies}}=42* 1.32`

`\text{Earnings from selling 42 fruit pies}}=55.44`

Therefore, earnings of Mr. Sanchez's class from selling 42 fruit pies will be $55.44.

As $84.96 is greater than $55.44, therefore, Mr. Kelly's class earned more money.

(c) To find the amount of more money earned by Mr. Kelly's class let us subtract earnings of Mr. Sanchez's class from earnings of Mr. Kelly's class.

`\text{The amount of more money earned by Mr. Kelly's class}=\$84.96-\$55.44`

`\text{The amount of more money earned by Mr. Kelly's class}=\$29.52`

Therefore Mr. Kelly, class earned $29.52 more than Mr. Sanchez's class.