# Solving a Word Problem on Proportions Using a Unit Rate

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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?

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\$