00:02: In this exercise, we will see how a proportion can be applied to solve a word problem. A proportion sets two ratios equal to each other. We can use this proportional relationship to solve for an unknown quantity. 00:14: Let's work a problem by setting up a proportion and solving for an unknown quantity. A man used 12 gallons of gasoline on a 160-mile trip. How many gallons of gasoline will he use on a 400-mile trip? First, we want to define the unknown quantity. So we let X represent the number of gallons of gasoline used on a 400-mile trip. Next, we need to set up a ratio using the known right and the problem. The ratio is 160 miles to 12 gallons. Then we set up the ratio with the unknown quantity. The ratio is 400 miles to X gallons. Notice that the same units occupy corresponding positions in the ratios. Therefore, we can set up a proportion using these ratios to solve for the unknown quantity of X gallons. The proportion is 160 miles over 12 gallons equals 400 miles over X gallons. We dropped the units and solve for X by cross multiplying. This gives us 160 X equals 12 times 400, which gives us X equaling 30. Therefore, on a 400-mile trip, the man will use 30 gallons of gas.

Question

Which variable was used to define the unknown quantity?
Responses
A xx
B yy
C zz
Question 2
Which ratio was used for the given rate?
Responses
A 160/12160/12
B 12/16012/160
Question 3
How many gallons of gasoline will be used on a 400-mile trip?
Responses
A 2020
B 30

Answer 1

Here are the answers to your questions:

Question 1
Which variable was used to define the unknown quantity?
Response: A) x

Question 2
Which ratio was used for the given rate?
Response: A) 160/12

Question 3
How many gallons of gasoline will be used on a 400-mile trip?
Response: B) 30