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.
Method (to solve proportions WP’s) 1 Make sure it really is a proportional situation. 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!)
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
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
Example 1 Duncan travels 150 km in 1. 5 hours. Donovan travels 7 hours at the same rate. How far does Donovan travel? km km Solution: 150 h 1. 5 7 If “km” is on the top of the 1 st ratio. It must also be on top of the 2 nd ratio h
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 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.
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 150 1. 5 7 100 Donovan travels 700 km.
Example 2 Two identical cars cost $24 000. 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
Example 2 Two identical cars cost $24 000. If you bought 12 of these cars, how much would it cost? Solution: #cars 2 $ 12 24000 If “# cars” is on the top of the 1 st ratio. It must also be on top of the 2 nd ratio $
Example 2 Two identical cars cost $24 000. If you bought 12 of these cars, how much would it cost? Solution: 2 24000 The cars cost $144 000. 12
Example 2 Two identical cars cost $24 000. If you bought 12 of these cars, how much would it cost? Solution: Check: Is $144 000 a reasonable answer? 12 cars is greater than 2 cars… …so, the answer should be greater than $24 000! The cars cost $144 000.
Example 2 Two identical cars cost $24 000. If you bought 12 of these cars, how much would it cost? Solution: Check: Is 2 24000 144 000 0. 000083 The cars cost $144 000.
Example 3 Josh’s new house is 5/6 complete. If he has spent $175 000 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
Example 3 Josh’s new house is 5/6 complete. If he has spent $175 000 so far, what is the total amount of money he will spend on the house? Solution: now 5 later 175000 6 If “now” is on the top of the 1 st ratio. It must also be on top of the 2 nd ratio later
Example 3 Josh’s new house is 5/6 complete. If he has spent $175 000 so far, what is the total amount of money he will spend on the house? Solution: 5 6 The total will be $210 000. 175000
Example 3 Josh’s new house is 5/6 complete. If he has spent $175 000 so far, what is the total amount of money he will spend on the house? Solution: Check: Is $210 000 a reasonable answer? When 5/6 complete it is $175000… …so, when complete it should cost more! The total will be $210 000.
Example 3 Josh’s new house is 5/6 complete. If he has spent $175 000 so far, what is the total amount of money he will spend on the house? Solution: Check: Is 5 6 0. 8333 The total will be $210 000. 210 000 0. 8333
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