Proportions Word Problems

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Presentation transcript:

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) 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!)

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 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

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.

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: 150 Check: Is 1.5 7 100 100 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 #cars 2 12 24000 $ $ If “# cars” is on the top of the 1st ratio. It must also be on top of the 2nd ratio

Example 2 Two identical cars cost $24 000. If you bought 12 of these cars, how much would it cost? Solution: 2 12 24000 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 $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: 2 Is Check: 24000 144 000 0.000083 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 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

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 175000 6 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 $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: 5 Is Check: 6 210 000 0.8333 0.8333 The total will be $210 000.