Let's go through each question one by one:
Question 1
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. For every 2 cups of sugar, 3 cups of flour are needed.
If 16 cups of sugar are used: \[ \text{flour} = \left( \frac{3}{2} \right) \times 16 = 24 \text{ cups} \]
Answer: 24
Question 2
If \( y = 4 \) when \( x = 3 \), what is the value of \( y \) when \( x = 9 \)? The ratio is \( \frac{y}{x} = \frac{4}{3} \). To find \( y \) when \( x = 9 \):
\[ y = \frac{4}{3} \times 9 = 12 \]
Answer: 12
Question 3
What is the constant of proportionality if \( y = 24 \) when \( x = 8 \)? The constant of proportionality \( k \) is given by: \[ k = \frac{y}{x} = \frac{24}{8} = 3 \]
Answer: 3
Question 4
How long will it take Alex to mow 35 lawns if he can mow 5 lawns in 6 hours? The rate is: \[ \text{Rate} = \frac{5 \text{ lawns}}{6 \text{ hours}} \Rightarrow \text{ To mow 35 lawns: } \]
Total time needed: \[ \text{Time} = \frac{35 \text{ lawns}}{5 \text{ lawns}} \times 6 \text{ hours} = 42 \text{ hours} \]
Answer: 42 hours
Question 5
If Ana runs 5k races (3 miles each) for 4 hours, how many miles has she run? Duration of each race = 30 minutes or 0.5 hours. Number of races in 4 hours: \[ \text{Number of races} = \frac{4 \text{ hours}}{0.5 \text{ hours}} = 8 \] Total miles run: \[ \text{Total miles} = 8 \times 3 = 24 \text{ miles} \]
Answer: 24 miles
Question 6
How many pints of orange paint are needed if 18 pints of yellow paint are used? The ratio of orange to yellow paint is 4:6, which simplifies to 2:3.
For 18 pints of yellow: \[ \text{orange} = \left( \frac{2}{3} \right) \times 18 = 12 \text{ pints} \]
Answer: 12
Question 7
If \( y = 5 \) when \( x = 11 \), what is \( y \) when \( x = 88 \)? The ratio is: \[ \frac{y}{x} = \frac{5}{11} \] So when \( x = 88 \): \[ y = \frac{5}{11} \times 88 = 40 \]
Answer: 40
Question 8
What is the constant of proportionality if \( y = 48 \) 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, how much will the shoes cost if she needs to babysit for 28 hours? To find the total earnings: \[ \text{Earnings per hour} = \frac{21}{4} = 5.25 \] For 28 hours: \[ \text{Total money} = 5.25 \times 28 = 147 \]
Answer: $147
Question 10
How many skeins of pink yarn are needed if Josie uses 2 skeins of pink yarn for every 3 skeins of blue yarn and uses 18 skeins of blue? The ratio of pink to blue yarn is 2:3.
So for 18 skeins of blue: \[ \text{pink} = \left( \frac{2}{3} \right) \times 18 = 12 \]
Answer: 12
Summary of Answers
- 24
- 12
- 3
- 42 hours
- 24 miles
- 12
- 40
- 4
- $147
- 12