How much of each candy

Question

the parents like caramels($1.5/lb.) and the kids like gummy bears($2/lb). combined, they bought a 1.25lb bag that cost $2.50. How much of each candy did they buy?

Answer 1

Let C = pounds of caramels purchased and G = pounds of gummy bears purchased.

$1.50C+$2G =$2.50 assuming the per pound price remains the same in a mixed bag

1.5C+2G=2.5 cancel out the dollar signs

and C+G=1.25 they both have to add up to 1.25 pounds

C=1.25-G solve for either C or G and then substitute into the first equation

1.5(1.25-G) + 2G = 2.5 expand and simplify

1.875 - 1.5G +2G =2.5

.5G = 2.5-1.875 = 0.625

G=2(.625) = 1.25 pounds C=zero pounds

Buying all gummy bears at $2 per pound means buying 1.25 pounds times $2 = $2.50

the "mixed" bag is all gummy bears and no caramels. IF any caramels were purchased, then the total price for 1.25 mixed bag would be less than $2.50 The only way the purchase price could be as high as $2.50 is if it's a bag of only gummy bears.