Question

A recipe calls for 6 cups of flour for every 4 cups of sugar. How many cups of flour are needed if 16 cups of sugar are used?(1 point) Responses 24 24 18 18 16 16 12 12 Question 2 In a proportional relationship, if ( y = 4 ) when ( x = 3 ), what is the value of ( y ) when ( x = 9 )?(1 point) Responses 8 8 10 10 12 12 14 14 Question 3 If (y) is directly proportional to (x) and (y=24) when (x=8), what is the constant of proportionality?(1 point) Responses 12 12 10 10 9 9 3 3 Question 4 Alex is mowing lawns to earn money to buy a new gaming system and knows he needs to mow 35 lawns to earn enough money. If he can mow 5 lawns in 6 hours, how many how long will it take him to mow 35 lawns? Assume that he can mow each lawn in the same amount of time.(1 point) Responses 40 hours 40 hours 42 hours 42 hours 44 hours 44 hours 46 hours 46 hours Question 5 Ana runs 5k races which are about 3 miles each. She usually finishes each race in about 30 minutes. If she ran for 4 hours so far this year while completing 5k races, how many miles has she run?(1 point) Responses 18 miles 18 miles 20 miles 20 miles 22 miles 22 miles 24 miles 24 miles Question 6 A project uses for 4 pints of orange paint for every 6 pints of yellow paint. How many pints of orange paint are needed if 18 pints of yellow paint are used?(1 point) Responses 12 12 8 8 16 16 10 10 Question 7 In a proportional relationship, if ( y = 5 ) when ( x = 11 ), what is the value of ( y ) when ( x = 88)?(1 point) Responses 20 20 40 40 60 60 80 80 Question 8 If (y) is directly proportional to (x) and (y=48) when (x=12), what is the constant of proportionality?(1 point) Responses 2 2 3 3 4 4 6 6 Question 9 Kendra is babysitting to earn money to buy a new pair of shoes and knows she needs to babysit for 28 hours to earn enough money. If she can earn $21 for 4 hours of babysitting, how much will the shoes cost?(1 point) Responses $48 $48 $147 $147 $96 $96 $162 $162 Question 10 Josie uses 2 skeins of pink yarn for every 3 skeins of blue yarn while knitting a baby blanket. How many skeins of pink yarn are needed if she 18 skeins of blue yarn to complete the blanket?(1 point) Responses 9 9 10 10 11 11 12

Answer 1

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

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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

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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

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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

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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

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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

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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

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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

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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

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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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