GED Mathematical Reasoning TestQuantitative Problem Solving with Rational NumbersMedium
A baker uses a recipe that calls for 3/4 cup of sugar for every 2 cups of flour. If the baker has 5 cups of sugar, how much flour is needed to maintain the same ratio?
- A13 1/3 cups
- B7 1/2 cups
- C6 2/3 cups
- D3 3/4 cups
Show answer & explanationAnswer & explanation
Correct answer: A. 13 1/3 cups
Set up a proportion: (3/4 cup sugar) / (2 cups flour) = (5 cups sugar) / (x cups flour). Cross-multiply to solve for x: (3/4)x = 2 * 5. So, (3/4)x = 10. Multiply both sides by (4/3): x = 10 * (4/3) = 40/3 = 13 1/3 cups of flour.
Why the other options are wrong
- B. Incorrect. This might arise from 5 multiplied by 1.5, confusing the ratio.
- C. Incorrect. This would be the amount of sugar needed if you had 5 cups of flour.
- D. Incorrect. This might arise from multiplying 5 by 3/4.
Solving Proportions with Fractions
A proportion is an equation stating that two ratios are equal. To solve for an unknown in a proportion involving fractions, cross-multiplication is often used.
- Set up two equivalent ratios as a proportion.
- Place the unknown variable (x) in the appropriate position.
- Cross-multiply the terms.
- Solve the resulting linear equation for x.
Memory trick: Ratios balance like scales; cross-multiply to find the missing piece.