Ratio and Proportion Challenge Problems
Ratio and Proportion Enrichment Questions: NCTM
Grade 7 Ratio Proportion & Percent Challenge Problems
2007
2m. If 8 mathletes can solve 20 problems in 10 minutes, how many mathletes would it take to solve 30 problems in 5 minutes? Assume all mathletes solve problems at the same rate.
2008
2ar. When times got tough at Unit Cubes math supply shop, the owner temporarily cut everyone’s salary by 20%. Later, when business picked up, he raised these temporary salaries by 20% to give everyone their new salary. What percent were people’s new salaries greater than or less than their original salaries? Give your answer to the nearest percent, using a negative or a positive sign as appropriate.
2009
1m. Madison has 6 green, 6 purple and 6 blue marbles in a jar. She is going to take marbles out of the jar so that the marbles that are left fit these facts.
Facts:
• 1 out of every 3 marbles is green.
• 1 out of every 4 marbles is purple.
• 5 out of every 12 marbles are blue.
How many marbles will Madison take out of the jar?
3m. The height of the Statue of Liberty is 92 meters. There are 2.54 centimeters in an inch, 100 cm in a meter, 12 inches in a foot, and 3 feet in a yard. If the Statue of Liberty were to lie down on a 100yard football field, with her feet at the 0 yard line of one side, how far would the statue stick into the end zone of the other side of the field?
3ar. Eleanor signed a contract for a starting salary of $43,500 with a guaranteed raise of 2.5% for each of the next seven years. How much will her salary be after the seventh raise? Express your answer to the nearest whole number of dollars.
Solutions 2007
2m. If the 8 mathletes can solve 20 problems in 10 minutes, then they would only solve 10 problems in 5 minutes. If we want 30 problems solved in that amount of time, it will take 3 times as many mathletes, which is 3 8 = 24 mathletes.
Solutions 2008
2ar. A 20% cut in pay means the employees get 80% of their original salaries. When the salaries are raised by 20% later on, they get 120% of the reduced salaries. In the end, they get only 0.8 1.2 = 0.96 or 96% of their original salaries. This is 4% less, or –4%.
Solutions 2009
1m. If 5/12 of the marbles are to be blue, then there can only be 12 marbles in all. Madison will take 18 – 12 = 6 marbles out of the jar.
3m. 92 meters 100 = 9200 centimeters. 9200 cm ÷ 2.54 cm per inch = 3622 inches. 3622 in ÷ 12 in per foot = 301.837 feet. Subtract the 300 feet of the field to get 1.837 feet. 0.837 feet 12 in per foot = 10 inches. So the statue of liberty would sick 1 foot 10 inches into the end zone.
3ar. Each time Eleanor gets a raise of 2.5%, we will multiply her salary by 1.025. After 7 raises, her salary will be $43,500 1.0257 ≈ $43,500 1.1887 ≈ $51,708 to the nearest whole number of dollars.
