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.