Question

The yearbook club is having a bake sale to raise money for the senior class. Large cupcakes are sold for $1.25 each and small cupcakes are sold for $0.75 each. If 105 cupcakes were sold for a total amount of $109.75, how many large cupcakes did the yearbook club sell? A) 43 B) 55 C) 62 D) 16

So I know the answer is 62, but isn't this a question that can only be answered because we have the 4 multiple choice answers to test? Can this be figured out if we didn't have the answers?

Answer 1

This can be done with simple algebra, but I don't know if you have studied that already. If so ...

let the number of large cupcakes be x
let the number of small ones be y
x+y = 105 -----> y = 105-x

cost equation:
1.25x + .75y = 109.75
or, multiply each term by 100
125x + 75y = 10975
divide each term by 25
5x + 3y = 439
sub in the above value for y
5x + 3(105-x) = 439
5x + 315 - 3x = 439
2x = 124
x = 62 , which you had indicated was the correct answer.