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8 September, 01:15

adam prepares a meal of shrimp and brown rice. it must contain exactly 6 g of fat and 10 mg of iron. each 5oz serving of shrimp contains 2 g fat and 5 mg iron. each 1 cup of brown rice contains 6 g fat and 7 mg iron. how many servings of shrimp and brown rice should be in the meal?

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  1. 8 September, 05:14
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    Adam needs 9/8 of a 5oz serving of shrimps (which equals to 5.625 oz) and 5/8 of a cup of brown rice (which is around 10 tablespoons).

    Explanation:

    You are given:

    every serving of shrimp contains 2g of fat and 5mg of iron;

    every serving of rice contains 6g of fat and 7mg of iron;

    each meal should have 6g of total fat and 10mg of total iron.

    You need to set a system of equation: let's call

    s = quantity of shrimps

    r = quantity of rice

    The equation for the total fat will be: the quantity of fat in the serving of shrimps plus the quantity of fat in the serving of rice must be equal to 6g

    2s + 6r = 6 (1)

    Similarily:

    the quantity of iron in the serving of shrimps plus the quantity of iron in the serving of rice must be equal to 10g

    5s + 7r = 10 (2)

    In order to solve the system, solve for s in equation (1):

    s = (6-6r) / 2 = 3 - 3r (3)

    Substitute in equation (2):

    5 (3 - 3r) + 7r = 10

    and solve for r:

    15 - 15r + 7r = 10

    8r = 5

    r = 5/8

    Substitute the value of r in equation (3):

    s = 3 - 3*5/8 = 9/8

    Therefore Adam would need 9/8 of a 5oz serving of shrimps and 5/8 of a 1 cup of brown rice for each meal.
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