Question

Jim sells candy bars to his family and friends as a fundraiser. The plain chocolate bars costs $1.50, and the king size chocolate bar costs $2.25. Jim sells a total of 55 candy bars, and earns a total $95.25. Write a system of equations and find out how many plain chocolate bars he sold, and how many king size bars he sold.

Answer 1

38 plain chocolate bars and 17 king-size chocolate bars.

Explanation:

Let's define the variables:

P = number of plain chocolate bars sold

K = number of king chocolate bars sold

We know that each plain one costs $1.50, and each king one costs $2.25, then the total revenue is:

P*$1.50 + K*$2.25

Now we know that Jim sells a total of 55 candy bars, then:

P + K = 55

And we know that the total revenue is $95.25, then:

P*$1.50 + K*$2.25 = $95.25

Then we have the system of equations:

P + K = 55

P*$1.50 + K*$2.25 = $95.25

To solve this we need to isolate one of the variables in one of the equations, I will isolate P in the first equation to get:

P = 55 - K

Now we can replace is on the second one to get:

(55 - K)*$1.50 + K*$2.25 = $95.25

Now we can solve this for K

$82.50 - K*$1.50 + K*$2.25 = $95.25

K*($2.25 - $1.50) = $95.25 - $82.50 = $12.75

K*$0.75 = $12.75

K = $12.75/$0.75 = 17

This means that Jim sold 17 king-size chocolate bars.

Now we can replace this in the equation:

P + K = 55

P + 17 = 55

P = 55 - 17 =38

P = 38

Jim sold 38 plain chocolate bars.