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?
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.
Another way of approaching the problem is by setting up equations.
Let b= # of chocolate bars, and c=# 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(# of chocolate bars)+$0.75(# of gummy bears)=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:
b=132,c=143