Question

Mr. Sanchez’s class sold fruit pies for $1.65 each and Mr. Kelly’s class sold bottles of fruit juice for $1.36 each. Together, the classes sold 79 items and earned $118.17 for their school.
(1) Write and solve a system of equations that model the problem. Show all your work.
(2) Which class earned more money?
(3) How much more money did that class earn?

Answer 1

Answer:

Part A)

The system of equation is:

$\left\{ \begin{array}{ll}p+j=79\\ 1.65p+1.36j=118.17 \end{array}$

Solving it, we get that p, the number of fruit pies, is 37.

And j, the number of fruit juices, was 42.

Part B)

Mr. Sanchez’s class made more money. They made $61.05.

Mr. Kelly’s class made less money. They made $57.12

Part C)

So, Mr. Sanchez’s class made $3.93 more

Step-by-step explanation:

We will let p denote the amount of fruit pies sold and j denote the amount of fruit juices sold.

Mr. Sanchez’s class sold fruit pies for $1.65 each.

And Mr. Kelly’s class sold fruit juice for $1.36 each.

Part 1)

We know that in total, 79 items were sold. Therefore, the amount of fruit pies p plus the amount of fruit juices j sold must be 79. Therefore:

$p+j=79$

We also know that each fruit pie sells for $1.65.

So, for p fruit pies, the total earnings is 1.65p.

Each fruit juice sells for $1.36.

So, for j fruit juices, the total earnings is 1.36j.

We know that the total earnings was $118.17. This is the sum of the total earnings from the fruit pies as well as the total earnings from the fruit juices.

Therefore:

$1.65p+1.36j=118.17$

So, our system of equation is:

$\left\{ \begin{array}{ll}p+j=79\\ 1.65p+1.36j=118.17 \end{array}$

We can solve this using substitution.

From the first equation, let’s isolate a variable. We can subtract p from both sides. Therefore:

$j=79-p$

Now, we can substitute this into the second equation. So:

$1.65p+1.36(79-p)=118.17$

Now, we can solve for p.

Distribute the 1.36:

$1.65p-1.36p+107.44=118.17$

Subtract:

$0.29p+107.44=118.17$

Subtract 107.44 from both sides:

$0.29p=10.73$

Divide both sides by 0.29. So:

$p=37$

So, a total of 37 fruit pies were sold.

Now, we can solve for j:

$j=79-p$

Substituting 37 for p, we get:

$j=79-37=42$

Therefore, 37 fruit pies were sold by Mr. Sanchez’s class and 42 fruit juices were sold by Mr. Kelly’s class.

Part B)

Since each fruit pie was $1.65, Mr. Sanchez’s class made:

$\ 1.65(37)=\ 61.05$

Mr. Sanchez’s class made $61.05.

Since each fruit juice was $1.36, Mr. Kelly’s class made:

$1.36(42)=\ 57.12$

Mr. Kelly’s class made $57.12.

Therefore, Mr. Sanchez’s class made more money than Mr. Kelly’s class.

Part C)

To find out much more money Mr. Sanchez‘s class made than Mr. Kelly’s class, we can simply find the difference.

So, we will subtract Mr. Kelly’s earnings from Mr. Sanchez’s earnings. Therefore:

$D=61.05-57.12=\ 3.93$

So, Mr. Sanchez’s class mad $3.93 more than Mr. Kelly’s class.