college algebra

Question

By eating 1​ egg, 1​ cupcake, and 1 slice of​ pizza, a child consumes

300

mg of cholesterol. If the child eats

3

cupcakes and

4

slices of​ pizza, he or she takes in

82

mg of cholesterol. By eating

2

eggs and 1​ cupcake, a child consumes

568

mg of cholesterol. How much cholesterol is in each​ item?

Answer 1

e+c+p = 100

3c+4p = 82

2e+c = 568

subtract last equation from twice 1st equation

c+2p =32

multiply by 3 and subtract 2nd equation

2p=14

p =7 mg of cholesterol in a slice of pizza

c=32-14 = 18 mg cholesterol in cupcake

e = 300-25 = 275 mg cholesterol in an egg

check the answers

275+18+7 = 300

3(18)+4(7) =54+28 = 82

2(275)+18 =550+18 = 568