Proportional Relations & Measurement Conversions

Eight tickets to a concert cost $120.

What constant of proportionality relates the number of tickets to the total cost?

• $10 per ticket

• $12 per ticket

• $15 per ticket

• $20 per ticket

Answer explanation

To find the constant of proportionality that relates the number of tickets to the total cost, you can use the formula:

Constant of Proportionality = Total Cost / Number of Tickets

The constant of proportionality is:

120/8 = 5

So, the constant of proportionality is 15. This means that each ticket costs $15.

Tags

CCSS.7.RP.A.2B

There is a proportional relationship between the number of liters and the number of milliliters for liquid measurements. What constant of proportionality relates milliliters to liters?

1 liter (L) is equal to 1000 milliliters (mL).

• 0.001

• 0.01

• 10

• 1000

Answer explanation

There are 1,000 milliliters in 1 liter.

This means:

Number of Milliliters X Number of Liters

The constant of proportionality that relates milliliters to liters is 1,000.

Nine hundred thousand liters of water pass through a given point along a canal every hour.

Which equation represents the number of liters of water, y,

that pass through the point in x hours?

• y = 900,000x

• y = 90,000x

• y = 9,000x

• y = 900x

Answer explanation

• 900,000 liters of water pass through the point every hour.

This means that for each hour, x, 900,000 liters of water pass through.

The relationship can be expressed as:

y = 900,000 times x

So, the equation representing the number of liters of water, y, that pass through the point in x hours is:

y = 900,000x

Tags

CCSS.6.EE.C.9

The value of a comic book $10.50 began to increase once the series ended in 2000.

The value has increased by $3.75 each year since then.

How much was the comic book worth in 2020?

• $75.00

• $85.50

• $90.00

• $95.25

Answer explanation

To find out how much the comic book was worth in 2020, we need to calculate the total increase in value from 2000 to 2020 and then add that to the original value.

1. Calculate the number of years from 2000 to 2020: 2020 - 2000 = 20

3. Calculate the total increase in value:

4. 20 X $3.75 = $75

6. Add the total increase to the original value:

7. $10.50 + $75 = $85.50

So, the comic book was worth $85.50 in 2020.

Tags

CCSS.HSF.BF.A.2

Approximately how many yards are equivalent to 12 kilometers?

1 kilometer is approximately equal to 1,093.61 yards.

• 10,936 yards

• 12,000 yards

• 13,123 yards

• 14,000 yards

Answer explanation

To convert 12 kilometers to yards, you can use the given conversion factor:

1 kilometer = 1,093.61 yards

So, for 12 kilometers:

12 kilometers X 1,093.61 = 13,123.32 yards}

Tags

CCSS.5.MD.A.1

John is 162 centimeters tall. How tall is John in inches?

Round to the nearest tenth inch.

1 centimeter is approximately equal to 0.3937 inches.

• 64.2 inches

• 64.0 inches

• 63.8 inches

• 63.5 inches

Answer explanation

To convert John's height from centimeters to inches, you can use the given conversion factor:

1 centimeter = 0.3937 inches}

For 162 centimeters:

162 centimeters X 0.3937 inches = 63.7794 inches

Rounding to the nearest tenth:

63.7794 is approximately 63.8

John is approximately 63.8 inches tall.

Tags

CCSS.5.MD.A.1

Convert 5 gallons to liters and then use this information to determine how many liters are needed to fill a container that holds 10 gallons.

Which of the following is the correct amount of liters needed?

• 18.9 liters

• 20.0 liters

• 24.5 liters

• 37.8 liters

Answer explanation

To convert gallons to liters, you can use the conversion factor:

1 gallon = 3.78541 liters

Step 1: Convert 5 gallons to liters

5 gallons X 3.78541 liters = 18.92705 liters

So, 5 gallons is approximately 18.93 liters.

Step 2: Determine how many liters are needed to fill a 10-gallon container

10 gallons X 3.78541 liters = 37.8541 liters

You would need approximately 37.85 liters to fill a container that holds 10 gallons.

Tags

CCSS.5.MD.A.1

Carlos is driving to visit his grandparents. In 3 hours, he travels 135 miles. If he continues to travel at the same speed, which equation represents how far he will travel, d, in h hours?

• d = 45h

• d = 40h

• d = 50h

• d = 35h

Answer explanation

• Carlos travels 135 miles in 3 hours.

First, calculate his speed (miles per hour):

Speed = Distance / Time

135 / 3 = 45 miles per hour

Now, we can use this speed to write the equation for the distance ( d ) he will travel in ( h ) hours:

d = 45h

Tags

CCSS.6.EE.C.9

Ms. Johnson's science class is raising ladybugs. One of the ladybugs weighs 3.7 ounces. About how many grams does the ladybug weigh? Round to the nearest tenth of a gram.

1 ounce is approximately equal to 28.3495 grams.

• 104.9 grams

• 105.0 grams

• 106.5 grams

• 107.2 grams

Answer explanation

To convert the weight of the ladybug from ounces to grams, you can use the given conversion factor:

1 ounce = 28.3495 grams

So, for 3.7 ounces:

3.7 ounces X 28.3495 grams = 104.69315 grams

Rounding to the nearest tenth:

104.69315 is approximately 104.7

The ladybug weighs approximately 104.7 grams.

Tags

CCSS.6.RP.A.3D

Alex buys 5 dozen pencils for $8.50.

What is the cost of 15 dozen pencils?

• $27.50

• $26.00

• $24.00

• $25.50

Answer explanation

To find the cost of 15 dozen pencils, we first need to determine the cost per dozen pencils and then use that to calculate the total cost for 15 dozen.

Step 1: Calculate the cost per dozen pencils

5 dozen pencils cost $8.50

$8.50 / 5 = $1.70 per dozen

Step 2: Calculate the cost for 15 dozen pencils

15 X $1.70 = $25.50

The cost of 15 dozen pencils is $25.50.

Tags

CCSS.6.RP.A.3B