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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?

 Feb 17, 2020
 #1
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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

 

 

 

cool cool cool

 Feb 17, 2020

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