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10 January, 14:57

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?

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  1. 10 January, 18:37
    0
    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
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