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?
+24 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.
+998 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:
\(\boxed{b = 132 , c = 143}\)
