Victory for the ACT Student Text 15e

L ESSON 1 | N UMBER AND Q UANTITY • 213 32. The cost of picture framing depends on the outer perimeter of the frame. If a 15-inch-by-15-inch picture frame costs $35 more than a 10-inch-by-10-inch picture frame, what is the cost of framing, in dollars per inch? F. $3.50 G. $2.75 H. $2.25 J. $1.75 K. $1.50 33. Walking at a constant speed of 4 miles per hour, it took Jill exactly 1 hour to walk home from school. If she walked at a constant speed of 5 miles per hour, how many minutes would the trip take? A. 48 B. 54 C. 56 D. 72 E. 112 34. Ms. Peters drove from her home to the park at an average speed of 30 miles per hour and returned home along the same route at an average speed of 40 miles per hour. If her driving time from home to the park was 20 minutes, how many minutes did it take Ms. Peters to drive from the park to her home? F. 7.5 G. 12 H. 15 J. 24 K. 30

29. Clyde drove at a constant rate of speed for 4 hours and covered a distance of 200 miles. If he had driven at the same rate for 5 hours, how many miles would he have driven? A. 160 B. 180 C. 200 D. 220 E. 250 30. At Star Lake Middle School, 45% of the students bought a yearbook. If 540 students bought yearbooks, how many students did NOT buy a yearbook? F. 243 G. 540 H. 575 J. 660 K. 957 31. A train traveling at a constant speed, k , takes 90 minutes to go from point P to point Q , a distance of 45 miles. What is the value of k , in miles per hour? A. 20 B. 30 C. 45 D. 60 E. 75

The Cambridge Edge To solve rate problems, create expressions of rates in which the units cancel leaving a quantity in the desired units. This is true for any problem involving rates, measurements, and unit conversions. The Cambridge Edge Notice the thought-reverser NOT in item #30. Remember to keep the thought- reverser in mind when selecting ›‘—” ϐ‹ƒŽ ƒ•™‡”Ǥ

Throwback to Math Class When setting up proportions, a common technique for solving for an unknown is cross-multiplying . Cross-multiplying is when you multiply the numerator of the ϐ‹”•– ˆ”ƒ…–‹‘ ™‹–Š –Š‡ †‡‘‹ƒ–‘” ‘ˆ –Š‡ •‡…‘† ƒ† –Š‡ †‡‘‹ƒ–‘” ‘ˆ –Š‡ ϐ‹”•– fraction with the numerator of the second and set both products equal to each other. Cross-multiplying eliminates the fractions and returns an equation that is easy to solve algebraically.