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The band club is selling chocolate bars and gummy candy to make money for their summer trip. Add a recent fundraiser day the club made $272.25 and sold a total of 275 chocolate bars and gummy candies. If chocolate for sale for$1.25 a gummy's sale for \$.75 how many of each did they sale?

Mar 4, 2020

#1
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I first abbreviated chocolate bars for cb and gummy candies for gc. I started with Cb+gc=275. I used guess and check for this one. Let's start off with 100 Chocolate bars. This amounts to 125+131.25 = 256.25. This shows that you need more chocolate bars. Each gummy candy you switch into a chocolate bar will add 0.5 dollars to your total bill. You subtracted 272.25 from 256.25, and you get 16. 16 is 32 halves of a dollar. This means you need 32 more Chocolate bars. This amounts to a total of 100+32 = 132 chocolate bars and 143 gummy candies.

Mar 4, 2020
#2
+886
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Another way of approaching the problem is by setting up equations.

Let $$b = \text{ # of chocolate bars}$$, and $$c = \text{# of gummy candy}$$

Because the total number of bars and candies sold was $$275$$,

We can set up the equation $$b + c = 275$$

Next, we have the individual price for the chocolate bars, the individual price for the gummies, and the total price. We can set up another equation using these three.

$$1.25 ( \text{# of chocolate bars} ) + 0.75 ( \text{# of gummy bears} ) = \text{total price}$$,

Therefore,

$$1.25b + 0.75c = 272.25$$

Now we have our two equations,

$$b + c = 275$$

$$1.25b + 0.75c = 272.25$$

You can either use substitution or elimination to solve for the two equations,

Which leaves us with our final answers:

$$\boxed{b = 132 , c = 143}$$

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Mar 4, 2020