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?

cholesterol in egg = 273 mg

cholesterol in cupcake = 18 mg

cholesterol in slice of pizza = 9 mg

Step-by-step explanation:

Given dа ta:

1 egg, 1 cupcake, 1 slice of pizza = 300mg

3 cupcakes, 4 slices of pizza = 90mg

2 eggs, 1 cupcake = 564mg

Let egg be x, let cupcake be y and let pizza be y

x + y + z = 300 (equation 1)

0x + 3y + 4z = 90 (equation 2)

2x + y + 0z = 564 (equation 3)

Using equation 1 and equation 2

x + y + z = 300 (Multiply equation by 3)

0x + 3y + 4z = 90

3x + 3y + 3z = 900

0x + 3y + 4z = 90 (Subtracting the equations)

3x - z = 810 (equation 4)

Using equation 2 and equation 3

0x + 3y + 4z = 90

2x + y + 0z = 564 (Multiply equation by 3)

0x + 3y + 4z = 90

6x + 3y + 0z = 1692 (Subtracting the equations)

-6x + 4z = -1602 (equation 5)

Solving equation 4 and equation 5

3x - z = 810 therefore z = 3x - 810

Substituting z into equation 5

-6x + 4 (3x - 810) = -1602

-6x + 12x - 3240 = - 1602

6x = - 1602+3240

6x = 1638

x = 273

Substituting x into z = 3x - 810

z = 3 (273) - 810

z = 819-810

z = 9

Using equation 1 to find y

x + y + z = 300

273 + y + 9 = 300

282 + y = 300

y = 300-282

y = 18