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

Try the following problems:

 1. A soccer team played 25 games and won 17. a.  What is the ratio of the number of wins to the number of loses? b.  What is the ratio of the number of games played to the number of games won? Answer a 17:8 Explanation Played 25, won 17 therefore they lost 8. Answer b 25:17

 2 In a senior class, there are b boys and g girls.  Express the ratio of the number of boys to the total number in the class. Answer b/(b+g)

 3. Express this ratio in simplest form: Answer 7/17 or 7 : 17 Explanation The ratio changes to: 7/6 : 17/6 Which can be written 7/6 divided by 17/6 Which becomes 7/6 x 6/17 and reduces to 7/17 or 7 : 17.

 4 The Yankees won 125 games, the Red Sox won 97 games, and the Mets won 86 games.  What is the ratio of wins of the Yankees to the Red Sox to the Mets? Answer 125 : 97 : 86

 5. Two numbers are in a ratio of 5 : 3.  Their sum is 80.  Find the largest number. Answer 50 Explanation Let 5x be the first number. Let 3x be the second number. 5x + 3x = 80 8x = 80 x = 10 Substitute to find the largest number. 5(10) = 50

 6. Mr. Smith and Mr. Kelly are business partners.  They agreed to divide the profits in the ratio of 3 : 2.  The profit amounted to \$24,000.  How much did each person receive? Answer Smith \$14,400 Mr. Kelly \$9,600 Explanation Let 3x = Mr. Smith Let 2x = Mr. Kelly 3x + 2x = 24000 5x = 24000 x = 4800 3x = 3(4800) = 14400 2x = 2(4800)=9600

 7. The measures of the angles of a triangle are in the ratio of 2 : 3 : 4.  Find the number of degrees in the smallest angle of the triangle. Answer 40 degrees Explanation Represent the angles as 2x, 3x, and 4x. 2x + 3x + 4x = 180 9x = 180 x = 20 Since 2x represents the smallest angle, substitute to get the answer. 2(20) = 40 degrees.

 8. Two angles of a triangle are in the ratio of 3 : 5.  The difference of the angles is 30 degrees.  Find the number of degrees in the largest angle in the triangle. Answer 75 degrees Explanation Represent the angles by 3x and 5x. 5x - 3x = 30 2x = 30 x = 15 The angles of the triangle are 3(15) = 45 degrees 5(15) = 75 degrees The third angle is 180 - 45 - 75 = 60. The largest angle is 75 degrees.

 9. What is the ratio of the circumference of a circle to its radius? Answer 2 pi Explanation The ratio of circumference to radius is 2 (pi) r to r which is [2(pi)r]/r. This reduces to [2 (pi)]/1 which is simply 2 pi.

 10. The length and width of a rectangle are in the ratio of 5 : 2.  Express in terms of x the perimeter of the rectangle. Answer 14x Explanation The length is represented by 5x and the width is represented by 2x. The perimeter would be 5x + 2x + 5x + 2x = 14x

 11. Hannah took a trip to visit her cousin.  She drove 120 miles to reach her cousin's house and the same distance back home.      a.  It took her 1.2 hours to get halfway to her cousin's house.  What was her average speed, in miles per hour, for the first 1.2 hours of her trip? b.  Hannah's average speed for the remainder of the trip to her cousin's house was 40 miles per hour.  How long, in hours, did it take her to drive the remaining distance? c.  Traveling home along the same route, Hannah drove at an average rate of 55 miles per hour.  After 2 hours her car broke down.  How many miles was she from home?

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