RATIO RATES AND PROPORTIONS WORKSHEET

Problem 1 :

The ratio of faculty members to students at a college is 1:15. There are 750 students. How many faculty members are there?

Problem 2 :

David ate 58.5 hot dogs in 13 minutes to win a contest. Find the unit rate in hot dogs per minute. Round to the nearest hundredth.

Problem 3 :

A large adult male human has about 12 pints of blood. Use dimensional analysis to convert this quantity to gallons.

Problem 4 :

The dwarf sea horse Hippocampus zosterae swims at a rate of 52.68 feet per hour. Use dimensional analysis to convert this speed to inches per minute.

Problem 5 :

Solve for x.

7/9 = 3/x

Problem 6 :

Solve for x.

5/9 = 10/(x + 2)

Problem 7 :

On a map with a scale of 1 in = 18 mi, the distance from Chicago to Evanston is 0.63 in. What is the actual distance ?

Problem 8 :

The actual distance between the two cities A and B is 54 mi. Find this distance on a map with a scale of 1 in = 18 mi. Round to the nearest tenth.

1. Answer :

Write a ratio comparing faculty to students.

Faculty ---> 1

Students ---> 15

Write a proportion. Let x be the number of faculty members.

x/750 = 1/15

Because x is divided by 750, multiply each side of the equation by 750.

750(x/750) = (1/15)750

x = 50

There are 45 faculty members.

2. Answer :

Write a proportion to find an equivalent ratio with a second quantity of 1.

58.5/13 = x/1

4.5 = x

The unit rate is approximately 4.46 hot dogs per minute.

3. Answer :

Step 1 :

Convert pints to quarts.

Multiply by a conversion factor whose first quantity is quarts and whose second quantity is pints.

12 pt ⋅ (1 qt/2 pt) = 6 qt

12 pints is 6 quarts.

Step 2 :

Convert quarts to gallons.

Multiply by a conversion factor whose first quantity is gallons and whose second quantity is quarts.

6 qt ⋅ (1 gal/4 qt) = 6/4 gal = 1½ gal

A large adult male human has about 1½ gallons of blood.

4. Answer :

Use the conversion factor 12 in./1 ft to convert feet to inches, and use the conversion factor 1 h/60 min to convert hours to minutes.

52.68 ft ⋅ 12 in. = 632.16 in.

1 hr ⋅ 60 min = 60 min

Then,

52.68 ft/1 hr = 632.16 in./60 min = 10.536 in./1 min

The speed is 10.536 inches per minute.

5. Answer :

7/9 = 3/x

Use cross products.

7x = 3(9)

7x = 27

Divide each side by 7.

x = 27/7

6. Answer :

5/9 = 10/(x + 2)

Use cross products.

5(x + 2) = 9(10)

5x + 10 = 90

Subtract 10 from each side.

5x = 80

Divide each side by 5.

x = 16

7. Answer :

Write the scale as a fraction.

map/actual = 1 in/ 18 mi

Let x be the actual distance.

1/18 = 0.63/x

Use cross products to solve.

1(x) = 18(0.63)

x = 11.34 miles

The actual distance is 11.34 miles.

8. Answer :

Write the scale as a fraction.

map/actual = 1 in/ 18 mi

Let x be the distance on a map.

x/54 = 1/18

Use cross products to solve.

18(x) = 54(1)

18x = 54

Divide each side by 18.

18x/18 = 54/18

x = 3

The distance on the map is 3 inches.

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