Questions: A glass of skim mik supplies 0.1 mg of iron and 8.3 g of protein. A quarter pound of lean meat provides 3.4 mg of iron and 23 g of protein. A person on a special diet is to have 10.7 mg of iror 110.5 g of protein. How many glasses of skim milk and how many quarter-pound servings of meat will provide this? How many glass(es) of skim milk and how many quarter-pound serving(s) of lean meat would be required?

A glass of skim mik supplies 0.1 mg of iron and 8.3 g of protein. A quarter pound of lean meat provides 3.4 mg of iron and 23 g of protein. A person on a special diet is to have 10.7 mg of iror 110.5 g of protein. How many glasses of skim milk and how many quarter-pound servings of meat will provide this? How many glass(es) of skim milk and how many quarter-pound serving(s) of lean meat would be required?
Transcript text: A glass of skim mik supplies 0.1 mg of iron and 8.3 g of protein. A quarter pound of lean meat provides 3.4 mg of iron and 23 g of protein. A person on a special diet is to have 10.7 mg of iror 110.5 g of protein. How many glasses of skim milk and how many quarter-pound servings of meat will provide this? How many glass(es) of skim milk and how many quarter-pound serving(s) of lean meat would be required?
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Solution

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Solution Steps

To solve this problem, we need to set up a system of linear equations based on the nutritional content of skim milk and lean meat. Let \( x \) be the number of glasses of skim milk and \( y \) be the number of quarter-pound servings of lean meat. We have two equations: one for iron and one for protein. Solve this system of equations to find the values of \( x \) and \( y \).

Step 1: Set Up the Equations

We define the variables:

  • Let \( x \) be the number of glasses of skim milk.
  • Let \( y \) be the number of quarter-pound servings of lean meat.

Based on the nutritional content, we can set up the following equations:

  1. For iron: \[ 0.1x + 3.4y = 10.7 \]
  2. For protein: \[ 8.3x + 23y = 110.5 \]
Step 2: Solve the System of Equations

By solving the system of equations, we find:

  • \( x = 5 \)
  • \( y = 3 \)

Final Answer

The required amounts are:

  • Glasses of skim milk: \( \boxed{x = 5} \)
  • Quarter-pound servings of lean meat: \( \boxed{y = 3} \)
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