solving applied problems

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 85 mg of cholesterol. by eating 2 eggs and 1 cupcake, a child consumes 567 mg of cholesterol. how much cholesterol is in each item?

Answer 1

E + C + P = 300

3C + 4P =85, 4P = 85-3C, P = (85-3C)/4

2E + C = 567, 2E = 567-C, E = (567-C)/2

(567-C)/2 + C + (85-3C)/4 = 300

multiply by 4

(567-C)2 + 4C + 85-3C = 1200

1134 -2C + 4C + 85 -3C = 1200

-C = 1200-85-1134

C =19mg for 1 cupcake

E = (567-C)/2 = (567-19)/2 = 274mg for one egg

P = (85-3C)/4 =7 mg for one pizza

C = 19, E =274, P = 7

19+274 + 7 = 300 mg