1. No, the number of hours is not proportional to the total cost because there is a fixed rental fee of $32 added to the hourly charge. The cost for 1 hour is $52, for 2 hours is $72, for 3 hours is $92, and for 4 hours is $112. The ratio of cost to hours is not constant (52/1 ≠ 72/2).
2. Yes, the number of cakes is proportional to the number of cups of sugar because the ratio is constant: 2 cups of sugar per cake. For 1 cake, 2 cups; for 2 cakes, 4 cups; for 3 cakes, 6 cups; for 4 cakes, 8 cups. The ratio sugar/cakes = 2 in all cases.
3. Yes, the number of CDs purchased is proportional to the cost because each CD costs $11.99. For 1 CD, $11.99; for 2 CDs, $23.98; for 3 CDs, $35.97; for 4 CDs, $47.96. The ratio cost/CDs = 11.99 in all cases.
4. No, the amount of money in Jean’s account is not proportional to the number of weeks because she starts with $280. After 1 week, she has $310; after 2 weeks, $340; after 3 weeks, $370; after 4 weeks, $400. The ratio savings/weeks is not constant (310/1 ≠ 340/2).
5. No, the relationship between Celsius and Fahrenheit is not proportional because the graph does not pass through the origin (0,0). When Celsius is 0, Fahrenheit is 32, so the ratio is undefined at zero and not constant across values.
6. Yes, the relationship between bags of popcorn and cost is proportional because the graph is a straight line passing through the origin (0,0), and the ratio cost/bags is constant: 4/1 = 8/2 = 12/3 = 16/4 = 4.
7. Yes, the total paid after each month is proportional to the number of months because the graph is a straight line passing through the origin (0,0), and the ratio cost/months is constant: $15 per month.
Parent Tip: Review the logic above to help your child master the concept of proportional and nonproportional relationships worksheet answers.
