1. Proportions Word Problems
When you are given a proportional situation as a word problem, often you will have to find a missing number.
This is another example of finding the missing term in a proportion.
So, we need a method to solve these types of problems.

2. Method (to solve proportions WP’s)
Make sure it really is a proportional situation. 1 2
Identify the quantities you know, and the quantity you need to find. (Check the units in the problem.) 3
Make a proportion. (Units must be consistent!)

3. Method (to solve proportions WP’s)4
Find the missing number in the proportion. (…by cross-multiplying or another method.) 5
CHECK YOUR ANSWER by:
a) Seeing if it “feels” right. b)
Plugging your answer back into the proportion & checking for equivalent ratios

4. Example 1
Duncan travels 150 km in 1.5 hours. Donovan travels 7 hours at the same rate. How far does Donovan travel?
Solution:
This is a proportional situation. (They tell you the rates are the same.)
Now, make a proportion

5. Example 1
Duncan travels 150 km in 1.5 hours. Donovan travels 7 hours at the same rate. How far does Donovan travel? km
Solution: km
150
1.5 7 h h
If “km” is on the top of the 1st ratio. It must also be on top of the 2nd ratio

6. Example 1
Duncan travels 150 km in 1.5 hours. Donovan travels 7 hours at the same rate. How far does Donovan travel?
Solution:
150
1.5 7
Donovan travels 700 km.

7. Example 1
Duncan travels 150 km in 1.5 hours. Donovan travels 7 hours at the same rate. How far does Donovan travel?
Solution:
Check:
Is 700 km a reasonable answer?
7 hours is greater than 1.5 hours
So, the answer should be greater than 150 km!
Donovan travels 700 km.

8. Example 1
Duncan travels 150 km in 1.5 hours. Donovan travels 7 hours at the same rate. How far does Donovan travel?
Solution:
150
Check: Is
1.5 7
100
100
Donovan travels 700 km.

9. Example 2
Two identical cars cost $ If you bought 12 of these cars, how much would it cost?
Solution:
This is a proportional situation. (If you double the # cars, this will double your total cost.)
Now, make a proportion

10. Example 2
Two identical cars cost $ If you bought 12 of these cars, how much would it cost?
Solution:
#cars
#cars 2 12
24000 $ $
If “# cars” is on the top of the 1st ratio. It must also be on top of the 2nd ratio

11. Example 2
Two identical cars cost $ If you bought 12 of these cars, how much would it cost?
Solution: 2 12
24000
The cars cost $

12. Example 2
Two identical cars cost $ If you bought 12 of these cars, how much would it cost?
Solution:
Check:
Is $ a reasonable answer?
12 cars is greater than 2 cars…
…so, the answer should be greater than $24 000!
The cars cost $

13. Example 2
Two identical cars cost $ If you bought 12 of these cars, how much would it cost?
Solution: 2 Is
Check:
24000
The cars cost $

14. Example 3
Josh’s new house is 5/6 complete. If he has spent $ so far, what is the total amount of money he will spend on the house?
Solution:
This is a proportional situation. (both ratios are 5 : 6)
Now, make a proportion

15. Example 3
Josh’s new house is 5/6 complete. If he has spent $ so far, what is the total amount of money he will spend on the house?
Solution:
now
now 5
175000 6
later
later
If “now” is on the top of the 1st ratio. It must also be on top of the 2nd ratio

16. Example 3
Josh’s new house is 5/6 complete. If he has spent $ so far, what is the total amount of money he will spend on the house?
Solution: 5
175000 6
The total will be $

17. Example 3
Josh’s new house is 5/6 complete. If he has spent $ so far, what is the total amount of money he will spend on the house?
Solution:
Check:
Is $ a reasonable answer?
When 5/6 complete it is $175000…
…so, when complete it should cost more!
The total will be $

18. Example 3
Josh’s new house is 5/6 complete. If he has spent $ so far, what is the total amount of money he will spend on the house?
Solution: 5 Is
Check: 6
0.8333
0.8333
The total will be $