Solving a Word Problem on Proportions Using a Unit Rate


Susan earned $135 for 9 hours of work. At the same rate, how many hours would she have to work to earn $180?

Solution

Step 1:

Amount earned in 9 hour = $ 135

Step 2:

Unit rate of earnings = $$\frac{135}{9}$ = $15 per hour

Step 3:

Number of hours to make $$180$ = $$\frac{180}{unit\: rate}$ = $$\frac{180}{15} = 12$ hours

At a comic book fair, a vendor sold a set of 9 comics for $76.50. How much it would cost to buy 4 such comics?

Solution

Step 1:

Cost of 9 comics = $76.50

Step 2:

Unit price of a comic book = $$\frac{76.50}{9}$ = $8.50

Step 3:

Cost of 4 comics = $4 \times $$$8.50 = $$$34.00$

An ice company charged $7.68 for 8 bags of ice. If a convenience store bought 7 bags of ice, what it would have cost them?

Solution

Step 1:

Cost of 8 bags of ice = $7.68

Step 2:

Unit price of a bag of ice = $$\frac{7.68}{8}$ = $0.96

Step 3:

Cost of 7 bags of ice = $7 \times 0.96$ = $$6.72$

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