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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