Here are the answers to the questions based on the provided information:
Question 1: To find out how many cups of flour are needed if 16 cups of sugar are used:
- The ratio of flour to sugar is 6:4, which simplifies to 3:2.
- If 2 cups of sugar correspond to 3 cups of flour, then:
- \( \frac{3 \text{ cups of flour}}{2 \text{ cups of sugar}} = \frac{x \text{ cups of flour}}{16 \text{ cups of sugar}} \)
- Cross multiplying, we get \( 2x = 48 \), so \( x = 24 \).
Answer: 24
Question 2: In a proportional relationship, if \( y = 4 \) when \( x = 3 \), then:
- The ratio is \( \frac{y}{x} = \frac{4}{3} \).
- To find \( y \) when \( x = 9 \):
- \( \frac{y}{9} = \frac{4}{3} \)
- Cross multiplying, \( 3y = 36 \), so \( y = 12 \).
Answer: 12
Question 3: If \( y \) is directly proportional to \( x \) and \( y = 24 \) when \( x = 8 \):
- The constant of proportionality \( k \) is found by \( k = \frac{y}{x} = \frac{24}{8} = 3 \).
Answer: 3
Question 4: Alex can mow 5 lawns in 6 hours. To find out how long it takes to mow 35 lawns, first find the time per lawn:
- \( \text{Time per lawn} = \frac{6 \text{ hours}}{5 \text{ lawns}} = 1.2 \text{ hours/lawn} \)
- Then for 35 lawns:
- \( 1.2 \text{ hours/lawn} \times 35 \text{ lawns} = 42 \text{ hours} \).
Answer: 42 hours
Question 5: If Ana runs 5k (3 miles) races in about 30 minutes, then in 4 hours (240 minutes):
- The number of races she can run in 240 minutes is \( \frac{240 \text{ minutes}}{30 \text{ minutes/race}} = 8 \text{ races} \).
- Therefore, miles run = \( 8 \text{ races} \times 3 \text{ miles/race} = 24 \text{ miles} \).
Answer: 24 miles
Question 6: If a project uses 4 pints of orange paint for every 6 pints of yellow paint:
- This simplifies to 2:3.
- For 18 pints of yellow paint, you set up the proportion: \( \frac{4 \text{ pints of orange}}{6 \text{ pints of yellow}} = \frac{x \text{ pints of orange}}{18} \).
- Cross multiplying gives \( 6x = 72 \), so \( x = 12 \).
Answer: 12
Question 7: If \( y = 5 \) when \( x = 11 \):
- The ratio is \( \frac{y}{x} = \frac{5}{11} \).
- To find \( y \) when \( x = 88 \):
- \( \frac{y}{88} = \frac{5}{11} \)
- Cross multiplying gives \( 11y = 440 \), so \( y = 40 \).
Answer: 40
Question 8: If \( y \) is directly proportional to \( x \) and \( y = 48 \) when \( x = 12 \):
- \( k = \frac{y}{x} = \frac{48}{12} = 4 \).
Answer: 4
Question 9: If Kendra can earn $21 for 4 hours of babysitting, then:
- The hourly rate is \( \frac{21}{4} = 5.25 \) dollars/hour.
- If she babysits for 28 hours:
- Total earnings will be \( 5.25 \text{ dollars/hour} \times 28 \text{ hours} = 147 \text{ dollars} \).
Answer: $147
Question 10: Josie uses 2 skeins of pink yarn for every 3 skeins of blue yarn:
- This simplifies to 2:3.
- For 18 skeins of blue yarn, the proportion becomes: \( \frac{2 \text{ skeins of pink}}{3 \text{ skeins of blue}} = \frac{x \text{ skeins of pink}}{18} \).
- Cross multiplying gives \( 3x = 36 \), so \( x = 12 \).
Answer: 12
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