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A glass of skim milk supplies 0.1 mg of iron and 8.6 g of protein. A quarter pound of

lean meat provides 3.5 mg of iron and 24 g of protein. A person on a special diet is to
have 7.5 mg of iron and 91.0 g of protein. How many glasses of skim milk and how
many quarter-pound servings of meat will provide this?

User Ian Kenney
by
9.2k points

1 Answer

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Let's assume x represents the number of glasses of skim milk and y represents the number of quarter-pound servings of lean meat.

We have the following information:

1 glass of skim milk supplies 0.1 mg of iron and 8.6 g of protein.

1 quarter pound of lean meat provides 3.5 mg of iron and 24 g of protein.

The person on a special diet needs 7.5 mg of iron and 91.0 g of protein.

We can set up the following system of equations based on the given information:

0.1x + 3.5y = 7.5 (for iron)

8.6x + 24y = 91.0 (for protein)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:

From the first equation, we can solve for x in terms of y:

0.1x = 7.5 - 3.5y

x = (7.5 - 3.5y) / 0.1

Substituting this value of x into the second equation, we get:

8.6[(7.5 - 3.5y) / 0.1] + 24y = 91.0

Simplifying:

86(7.5 - 3.5y) + 240y = 910

Expanding and rearranging:

645 - 301y + 240y = 910

-61y = 265

y = -265 / 61

y ≈ -4.34

Since the number of servings cannot be negative, we can conclude that y ≈ 4.34.

Substituting this value of y back into the equation for x:

x = (7.5 - 3.5(4.34)) / 0.1

x = (7.5 - 15.19) / 0.1

x ≈ -76.9 / 0.1

x ≈ -769

Again, the number of glasses cannot be negative, so x ≈ 769.

Since we cannot have fractional servings, we can round the values to the nearest whole number:

Approximately, 769 glasses of skim milk and 4 servings of quarter-pound lean meat will provide 7.5 mg of iron and 91.0 g of protein for the person on the special diet.

User Renanleandrof
by
8.6k points
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