Proportional Relationships practice questions

Proportional Relationships questions

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1. 1Proportional relationshipsFoundation

   If 0.4x = 18, what is x?If 0.4x = 18, what is x?

   • A7.27.2
   • B22.522.5
   • C4545
   • D7272
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   Answer: 4545

   Divide both sides by the coefficient: x = 180.4 = 45. Dividing by a decimal below 1 makes the result larger, which is the check that rules out 7.2.Divide both sides by the coefficient: x = 18/0.4 = 45. Dividing by a decimal below 1 makes the result larger, which is the check that rules out 7.2.

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2. 2Proportional relationshipsFoundation

   A machine fills 250 bottles in 20 minutes at a constant rate. Enter the number of bottles it fills in 50 minutes.A machine fills 250 bottles in 20 minutes at a constant rate. Enter the number of bottles it fills in 50 minutes.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 625625

   The rate is 25020 = 12.5 bottles per minute, and 12.5 × 50 = 625 bottles.The rate is 250/20 = 12.5 bottles per minute, and 12.5 × 50 = 625 bottles.

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3. 3Proportional relationshipsFoundation

   A recipe for 6 servings uses 300 grams of rice. How much rice is needed for 9 servings?A recipe for 6 servings uses 300 grams of rice. How much rice is needed for 9 servings?

   • A450 grams450 grams
   • B350 grams350 grams
   • C400 grams400 grams
   • D500 grams500 grams
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   Answer: 450 grams450 grams

   Find the unit rate first: 3006 = 50 grams a serving, so 9 servings need 50 × 9 = 450 grams. Scaling the original by 96 gives the same answer in one step.Find the unit rate first: 300/6 = 50 grams a serving, so 9 servings need 50 × 9 = 450 grams. Scaling the original by 9/6 gives the same answer in one step.

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4. 4Proportional relationshipsFoundation

   A car uses 6 liters of fuel for every 100 km driven. How much fuel does it use for 250 km?A car uses 6 liters of fuel for every 100 km driven. How much fuel does it use for 250 km?

   • A15 liters15 liters
   • B24 liters24 liters
   • C12 liters12 liters
   • D41.7 liters41.7 liters
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   Answer: 15 liters15 liters

   250 km is 2.5 lots of 100 km, so the fuel used is 2.5 × 6 = 15 liters. Dividing 250 by 6 gives 41.7, which answers how many 6-km stretches there are rather than how much fuel is burned.250 km is 2.5 lots of 100 km, so the fuel used is 2.5 × 6 = 15 liters. Dividing 250 by 6 gives 41.7, which answers how many 6-km stretches there are rather than how much fuel is burned.

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5. 5Proportional relationshipsFoundation

   Two lengths are in the ratio 3 : 5, and together they measure 96 cm. What is the shorter length?Two lengths are in the ratio 3 : 5, and together they measure 96 cm. What is the shorter length?

   • A60 cm60 cm
   • B36 cm36 cm
   • C32 cm32 cm
   • D48 cm48 cm
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   Answer: 36 cm36 cm

   The ratio has 3 + 5 = 8 parts, so each part is 968 = 12 cm and the shorter length is 3 × 12 = 36 cm. The choice 60 is the longer length and 48 is half the total.The ratio has 3 + 5 = 8 parts, so each part is 96/8 = 12 cm and the shorter length is 3 × 12 = 36 cm. The choice 60 is the longer length and 48 is half the total.

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6. 6Proportional relationshipsStandard

   A recipe uses 5 cups of flour to make 2 loaves of bread. At the same rate, enter the number of cups needed for 7 loaves.A recipe uses 5 cups of flour to make 2 loaves of bread. At the same rate, enter the number of cups needed for 7 loaves.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 17.517.5

   The rate is 52 = 2.5 cups per loaf. For 7 loaves, 2.5 × 7 = 17.5 cups.The rate is 5/2 = 2.5 cups per loaf. For 7 loaves, 2.5 × 7 = 17.5 cups.

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7. 7Proportional relationshipsStandard

   A map uses 1 inch to represent 25 miles. Enter the number of miles represented by 3.5 inches.A map uses 1 inch to represent 25 miles. Enter the number of miles represented by 3.5 inches.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 87.587.5

   Multiply the scale by the measured length: 25 × 3.5 = 87.5 miles.Multiply the scale by the measured length: 25 × 3.5 = 87.5 miles.

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8. 8Proportional relationshipsStandard

   If 5 workers build a wall in 12 days, enter how many days 4 workers would take at the same rate.If 5 workers build a wall in 12 days, enter how many days 4 workers would take at the same rate.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 1515

   The total work is 5 × 12 = 60 worker-days. Dividing by 4 workers gives 15 days. Fewer workers means more days, so the numbers move in opposite directions.The total work is 5 × 12 = 60 worker-days. Dividing by 4 workers gives 15 days. Fewer workers means more days, so the numbers move in opposite directions.

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9. 9Proportional relationshipsStandard

   On a map, 3 centimeters represents 12 kilometers. Enter the number of kilometers represented by 7.5 centimeters.On a map, 3 centimeters represents 12 kilometers. Enter the number of kilometers represented by 7.5 centimeters.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 3030

   The scale is 123 = 4 kilometers per centimeter, and 4 × 7.5 = 30 kilometers.The scale is 12/3 = 4 kilometers per centimeter, and 4 × 7.5 = 30 kilometers.

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10. 10Proportional relationshipsStandard

    A recipe uses 350 g of flour for 12 scones. How much flour is needed for 30 scones?A recipe uses 350 g of flour for 12 scones. How much flour is needed for 30 scones?

    • A840 g840 g
    • B1,050 g1,050 g
    • C875 g875 g
    • D292 g292 g
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    Answer: 875 g875 g

    Set up the proportion 35012 = x/30, so x = 350 × 30 = 10,500, and 10,50012 = 875 g. Tripling the 350 g gives 1,050, which would be right for 36 scones rather than 30.Set up the proportion 350/12 = x/30, so x = 350 × 30 = 10,500, and 10,500/12 = 875 g. Tripling the 350 g gives 1,050, which would be right for 36 scones rather than 30.

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11. 11Proportional relationshipsStandard

    A map is drawn to a scale of 1 cm to 25 km. Two towns are 14 cm apart on the map. Enter the distance between them in kilometers.A map is drawn to a scale of 1 cm to 25 km. Two towns are 14 cm apart on the map. Enter the distance between them in kilometers.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 350350

    Each centimeter stands for 25 km, so 14 cm stands for 14 × 25 = 350 km.Each centimeter stands for 25 km, so 14 cm stands for 14 × 25 = 350 km.

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12. 12Proportional relationshipsStandard

    Forty percent of a number is 26. Enter the number.Forty percent of a number is 26. Enter the number.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 6565

    If 0.40n = 26 then n = 260.40 = 65. Taking 40 percent of 26 answers the reverse question and gives 10.4.If 0.40n = 26 then n = 26/0.40 = 65. Taking 40 percent of 26 answers the reverse question and gives 10.4.

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13. 13Proportional relationshipsStandard

    Two amounts are in the ratio 2 : 7 and total 108. What is the larger amount?Two amounts are in the ratio 2 : 7 and total 108. What is the larger amount?

    • A8484
    • B9696
    • C2424
    • D5454
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    Answer: 8484

    The ratio has 9 parts, so each part is 1089 = 12 and the larger amount is 7 × 12 = 84. The smaller is 24, and the two sum to 108 as a check.The ratio has 9 parts, so each part is 108/9 = 12 and the larger amount is 7 × 12 = 84. The smaller is 24, and the two sum to 108 as a check.

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14. 14Proportional relationshipsStandard

    Two amounts are in the ratio 4 : 5 and total 153. What is the larger amount?Two amounts are in the ratio 4 : 5 and total 153. What is the larger amount?

    • A8585
    • B6868
    • C76.576.5
    • D9292
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    Answer: 8585

    The ratio has 9 parts, so each part is 1539 = 17 and the larger amount is 5 × 17 = 85. The smaller is 68, and the two sum to 153 as a check.The ratio has 9 parts, so each part is 153/9 = 17 and the larger amount is 5 × 17 = 85. The smaller is 68, and the two sum to 153 as a check.

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15. 15Proportional relationshipsChallenge

    If y varies directly with x and y = 18 when x = 4, enter the value of x when y = 45.If y varies directly with x and y = 18 when x = 4, enter the value of x when y = 45.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 1010

    Direct variation means y = kx with a constant k. From 18 = 4k, k = 4.5. Then 45 = 4.5x gives x = 10.Direct variation means y = kx with a constant k. From 18 = 4k, k = 4.5. Then 45 = 4.5x gives x = 10.

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