Question

Please help me with this question that were stuck on I am trying to help my son to understand but I am having trouble with breaking this down. He brought it back home from getting it wrong please help. I have attached a picture of the problemMr. Sanchez’s class sold fruit pies for $1.45 each and Mr. Kelly’s class sold bottles of fruit juice for $1.25 each. Together, the classes sold 53 items and earned $70.85 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

numberLet x be the number of fruit pies.

Let y be the quantity of juice bottles.

(a) Given the classes sold 53 items.

`\begin{gathered} x+y=53 \\ x=53-y\ldots\ldots(1) \end{gathered}`

Now, from the given data

`1.45x+1.25y=70.85\ldots\ldots(2)`

Substitute equation (1) in equation (2).

`\begin{gathered} 1.45(53-y)+1.25y=70.85 \\ 76.85-1.45y+1.25y=70.85 \\ 76.85-70.85=1.45y-1.25y \\ 0.20y=6 \end{gathered}`

Thus, the value of y will be

`\begin{gathered} y=(6)/(0.2) \\ y=30 \end{gathered}`

The bottle of fruit juice will be 30.

Calculate the value of x.

`\begin{gathered} x=53-30 \\ x=23 \end{gathered}`

The fruit pies will be 23.

(b) Now calculate which class earns more money.

Mr. Sanchez’s class

`\begin{gathered} 1.45x=1.45*23 \\ =33.35 \end{gathered}`

Mr. Kelly’s class

`\begin{gathered} 1.25y=1.25*30 \\ =37.5 \end{gathered}`

Therefore, Mr. Kelly’s class earned more money.

(c) How much more money did that class earn?

Find the difference

`37.5-33.35=4.15`