By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 300mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol. By eating 2 eggs and 1 cupcake, a child consumes 564 mg of cholesterol. How much cholesterol is in each item?
+128407 We have this system
E + C + P = 300 (1)
3C + 4P = 90 → 4P = 90 - 3C → [90 -3C ] / 4 = P (2)
2E + C = 564 → 2E = 564 - C → [ 564 - C ] / 2 = E (3)
Sub (2) and (3) into (1) and we have
[564 - C ] / 2 + C + [90 - 3C ] /4 = 300 multiply through by 4
1128 - 2C + 4C + 90 - 3C = 1200 simplify
1218 - C = 1200
C = 1218 - 1200 = 18mg in the cupcake
[90 -3 (18) ] / 4 = 36/4 = 9 mg in the pizza
[564 - 18] /2 = 273 mg in the egg
