Practice with Proportions Topic Index | Algebra Index | Regents Exam Prep Center

Try the following problems:

 1. Are the following true proportions? Answer a NO a. b. Answer b YES Explanation In part a, the product of the means does not equal the product of the extremes. (10 does not equal 30) In part b, it does. (30=30)

 2. Solve for x: Answer 28 Explanation Product of the means equals product of the extremes. 6x = 168 Divide both sides by 6. x = 28

 3. Solve for x: Answer 4 Explanation Product of means equals product of extremes. 15x = 5x + 40 Subtract 5x from both sides. 10x = 40 x = 4

 4. Solve for x: Answer x = 2rm/n Explanation Product of means equals product of extremes. 2xn = 4rm Divide both sides by 2n x = 4rm/2n x = 2rm/n

 5. If 4 tickets to a show cost \$9.00, find the cost of 14 tickets. Answer \$31.50 Explanation Let c = cost of the tickets 4/9 = 14/c 4c = 126 c = 31.5 c=\$31.50

 6. A house which is assessed for \$10,000 pays \$300 in taxes.  What should the tax be on a house assessed at \$15,500? Answer \$465 Explanation Let t = taxes 10000/300 = 15500/t 10000t = 4650000 t = \$465

 7. The length of the thruway is 600 miles.  If 0.5 inch represents 50 miles, what is the length of the thruway on the map? Answer 6 inches Intuitive Answer Divide 600 by 50 to determine the number of units.  600/50 = 12 units. Take the units and multiply by the scale. 12(0.5) = 6 inches Using a Proportion Establish a proportion: 0.5/50=x/600 50x = 300 x = 6 inches

 8. Solve for x: Answer x = 5 or x = -2 Explanation Cross multiply. x² - 3x = 10 x² - 3x - 10 = 0 Factor and solve. (x - 5)(x + 2) = 0 x = 5 or x = -2

 9. Solve for x: Answer x = -8 Explanation Cross multiply. 4x + 8 = 3x x = -8

 10. Maria is making pancakes for the annual pancake breakfast.  She needs two cups of batter to make eight 7-inch pancakes.  If Maria needs to make one thousand two hundred 7-inch pancakes, how many cups of batter does she need? Answer 300 cups Explanation Proportion: 2/8 = x/1200 8x = 2400 x = 300 cups of batter

 11. The dimensions of a building are 250 feet by 120 feet.  If 1 inch represents 20 feet on a scale drawing, what are the dimensions of the building on the drawing? Answer 12.5 in. by 6 in. Intuitive Answer Building 250 feet by 120 feet. 250 feet = 12.5 inches (HINT 250/20) 120 feet = 6 inches (HINT 120/20) Answer is 12.5 in. by 6 in. Using a Proportion Establish two proportions: Width: 1/20 = x/120 20x = 120 x = 6 inch Length: 1/20 = y/250 20y = 250 y=12.5 inch

 12. If on a scale drawing 48 feet are represented by 12 inches, then a scale of 1/4 inch represents how many feet? Answer 1 foot Explanation Let 1/4 = 0.25 You may use a proportion to solve this problem. 48/12 = x /.25 12x = 12 x = 1

 Topic Index | Algebra Index | Regents Exam Prep Center Created by Michael Caldwell