Practical Problems
Proportions: Word Problems
Direct Solving
Proportions: Set Up
Tax, Tip, Discount
100
The temperature in Wintergreen Resort in Virginia fell from 11.5 degrees Celsius to –6.7 degrees Celsius. What is the difference between the two temperatures?
18.2 degrees
(11.5 - -6.7 = 18.2)
100
If 2 inches is about 5.08 centimeters, about how many inches is 60 centimeters?
~23.6 inches
(I will also accept 24 inches)
100
4.5/x = 1/9
x = 40.5
100
A scale drawing of a basketball court uses a scale of 3 inches = 9.4 feet. The length of the basketball court in the scale drawing is 30 inches. Which proportion can be used to find the length of the actual court?
3/9.4 = x/30
3/9.4 = 30/x
30/3 = 9.4/x
B -
3/9.4 = 30/x
100
Katelyn received a 25% discount on the purchase of a $190 pair of shoes. What was the amount of the discount?
$47.50
(25% of 190 = 47.5 --> $47.50)
200
On Tuesday, the XYZ Company stock was at $10.70 per share. On Wednesday it gained $4.12, and then lost $8.80 on Wednesday. What is the new price per share?
$6.02
(10.70 + 4.12 - 8.80 = 6.02)
200
Carly made a scale drawing of her bedroom. The scale in the drawing is 3 inches represents 16 feet. The actual length of her bedroom is 40 feet. What is the length of her bedroom on the scale drawing?
7.5 inches
200
18% of 60
10.8
200
A scale drawing of a bus uses a scale of 1 inch = 6 feet. The length of the bus in the scale drawing is 22 inches. Which proportion can be used to find the length of the actual bus?
1/6 = 22/x
1/6 = x/22
1/22 = x/6
6/22 = 1/x
A -
1/6 = 22/x
200
Penny’s meal costs $52.82 at P.F. Chang’s. The server did their job very well and Penny would like to leave a 22% tip. What amount of money should he leave as a tip?
$11.62
(22% of 52.82 = 11.6204 --> 11.62)
300
A scuba diver was thirteen feet below the surface of the water and descended an additional twenty-two and a half feet. Eventually, the scuba diver ascended thirty feet toward the surface of the water.
What is the location of the scuba diver in the water?
5.5 feet below the water
(-30 - 22.5 + 30 = -5.5 OR 5.5 feet below the water)
300
The correct mixture of oil to gas in a lawn mower is 1/2 pint of oil to 1 1/2 gallons of gas. How many pints of oil are needed for 15 gallons of gas?
5 pints of oil
300
36/10 = x/5
x = 18
300
Mark is training for a half-marathon. He ran 8 miles on Saturday. One mile is equal to 5,280 feet. Which proportion can be used to determine how many feet, x, Max ran on Saturday?
1/5280 = x/8
1/8 = x/5280
1/5280 = 8/x
1/x = 5280/8
1/5280 = 8/x
300
The original price of a mini-refrigerator was $146.50. The tax on the mini-fridge was 5.5%. What is the exact price of the mini refrigerator including tax?
$154.56
(5.5% of 146.50 = 8.0575 -> 8.06 + 146.50 = 154.56)
400
Toby ran 5 1/2 miles. Phil ran half the distance that Toby ran. Yolanda ran a total of 5.75 miles. What was the total distance combined of all three runners?
14 miles
(show in DESMOS --> 5 1/2 + (5 1/2)/2 + 5.75 = 14)
400
Bayside Middle School is hosting their annual Winterfest Dance. The table shows how many chaperones will be needed, depending on how many students sign up.
Students 25 40 55
Chaperones 5 8 11
Using the proportional relationship in the table, how many chaperones will be needed for 80 students?
16 Chaperones
400
75% of 340
255
400
3.1 miles is about 5 kilometers. Which TWO proportions could be used to solve how many miles is about 10 kilometers?
5/10 = 3.1/x
3.1/10 = 5/x
3.1/5 = x/10
5/10 = x/3.1
5/10 = 3.1/x
3.1/5 = x/10
400
Jill went out to eat and her total, including tax, was $31.00. How much would she leave if she wanted to leave a 18% tip?
$36.58
(18% of 31 = 5.58 --> 5.58 + 31 = 36.58)
500
Jessica had 4 2/3 cups of sugar. A cookie recipe called for 3 1/3 cups of sugar. If Jessica made one batch of cookies, how much sugar did she have left over?
1 1/3
(4 2/3 - 3 1/3 = 1.3333 -> 1 1/3)
500
Larry wants to drive his Jeep around the coastline of Lake Tahoe. The scale factor of the map is 1 cm = 1.5 miles. He measured the distance around the lake on the map and it is 48 cm. What is the total distance, in miles, that Larry would drive his jeep around Lake Tahoe?
72 miles
1/1.5 = 48/x = 72
500
6/y = 18/30
y = 10
500
Jeff rode his bike around First Landing State Park's trail. He started at the West Entrance, headed toward the North Entrance, and ended back at the West Entrance. Based on the scale below, what proportion can be used to solve the problem?
1/1.5 = 20/x
1.5/1 = 20/x
1/1.5 = 9.5/x
A -
1/1.5 = 20/x
500
Jessie bought a $450 couch that was 30% off. What was the final price of the couch?
$315
(30% of 450 = 135 --> 450 - 135 = 315)