Question

For the fundraiser, Will sold 225 candy bars. He earns $1 for each almond candy bar he sells and $.75 for each caramel candy he sells. If he earned a total of $187.50 how many of each type of candy bar did he sell for the fundraiser?

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Answer 1

Will sold 75 almond candy bars and 150 caramel candy bars for the fundraiser. We used a system of equations to find that he sold two types of candy bars and we solved for the number of each type.

Step-by-step explanation:

To solve this problem, we need to set up a system of equations because there are two types of candy bars sold, almond and caramel. Will earns $1 for each almond candy bar and $0.75 for each caramel candy bar. The total number of candy bars sold is 225, and he earned $187.50 in total.

We can define the following variables:

• a for the number of almond candy bars sold
• c for the number of caramel candy bars sold

The following equations can represent the situation:

1. a + c = 225 (total number of candy bars sold)
2. $1 × a + $0.75 × c = $187.50 (total earnings from candy bars)

Let's multiply the second equation by 4 to eliminate the decimal, transforming it to:

1. 4 × ($1 × a + $0.75 × c) = 4 × $187.50
2. 4a + 3c = 750

This gives us the following system of equations:

1. a + c = 225
2. 4a + 3c = 750

Now we can multiply the first equation by 3:

1. 3a + 3c = 675

By subtracting this new equation from the second equation, we can find the value of a:

(4a + 3c) - (3a + 3c) = 750 - 675

a = 75

Now that we know a = 75, we can substitute this value back into the first equation to find c:

75 + c = 225

c = 150

Will sold 75 almond candy bars and 150 caramel candy bars for the fundraiser.