5.4E: Exercises
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More Practice: Number Problems
Set up a linear system and solve.
1. The sum of two integers is 45. The larger integer is 3 less than twice the smaller. Find the two integers.
2. The sum of two integers is 126. The larger is 18 less than 5 times the smaller. Find the two integers.
3. The sum of two integers is 41. When 3 times the smaller is subtracted from the larger the result is 17. Find the two integers.
4. The sum of two integers is 46. When the larger is subtracted from twice the smaller the result is 2. Find the two integers.
5. The difference of two integers is 11. When twice the larger is subtracted from 3 times the smaller, the result is 3. Find the integers.
6. The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers.
7. The sum of 3 times a larger integer and 2 times a smaller is 15. When 3 times the smaller integer is subtracted from twice the larger, the result is 23. Find the integers.
8. The sum of twice a larger integer and 3 times a smaller is 10. When the 4 times the smaller integer is added to the larger, the result is 0. Find the integers.
9. The difference of twice a smaller integer and 7 times a larger is 4. When 5 times the larger integer is subtracted from 3 times the smaller, the result is −5. Find the integers.
10. The difference of a smaller integer and twice a larger is 0. When 3 times the larger integer is subtracted from 2 times the smaller, the result is −5. Find the integers.
- Answer
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1. The integers are 16 and 29.
3. The integers are 6 and 35.
5. The integers are 25 and 36.
7. The integers are −3 and 7.
9. The integers are −5 and −2.
More Practice: Geometry Problems
1. The length of a rectangle is 5 more than twice its width. If the perimeter measures 46 meters, then find the dimensions of the rectangle.
2. The width of a rectangle is 2 centimeters less than one-half its length. If the perimeter measures 62 centimeters, then find the dimensions of the rectangle.
3. A partitioned rectangular pen next to a river is constructed with a total 136 feet of fencing (see illustration). If the outer fencing measures 114 feet, then find the dimensions of the pen.
4. A partitioned rectangular pen is constructed with a total 168 feet of fencing (see illustration). the perimeter measures 138 feet, then find the dimensions of the pen.
Add exercises text here.
- Answer
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1. Length: 17 meters; width: 6 meters 3. Width: 22 feet; length: 70 feet.
More Practice: Distance Problems
Set up a linear system and solve.
- The two legs of a 432-mile trip took 8 hours. The average speed for the first leg of the trip was 52 miles per hour and the average speed for the second leg of the trip was 60 miles per hour. How long did each leg of the trip take?
- Jerry took two buses on the 265-mile trip from Los Angeles to Las Vegas. The first bus averaged 55 miles per hour and the second bus was able to average 50 miles per hour. If the total trip took 5 hours, then how long was spent in each bus?
- An executive was able to average 48 miles per hour to the airport in her car and then board an airplane that averaged 210 miles per hour. The 549-mile business trip took 3 hours. How long did it take her to drive to the airport?
- Joe spends 1 hour each morning exercising by jogging and then cycling for a total of 15 miles. He is able to average 6 miles per hour jogging and 18 miles per hour cycling. How long does he spend jogging each morning?
- Swimming with the current Jack can swim 2.5 miles in 12 hour. Swimming back, against the same current, he can only swim 2 miles in the same amount of time. How fast is the current?
- A light aircraft flying with the wind can travel 180 miles in 112 hours. The aircraft can fly the same distance against the wind in 2 hours. Find the speed of the wind.
- A light airplane flying with the wind can travel 600 miles in 4 hours. On the return trip, against the wind, it will take 5 hours. What are the speeds of the airplane and of the wind?
- A boat can travel 15 miles with the current downstream in 114 hours. Returning upstream against the current, the boat can only travel 834 miles in the same amount of time. Find the speed of the current.
- Mary jogged the trail from her car to the cabin at the rate of 6 miles per hour. She then walked back to her car at a rate of 4 miles per hour. If the entire trip took 1 hour, then how long did it take her to walk back to her car?
- A jogger can sustain an average running rate of 8 miles per hour to his destination and 6 miles an hour on the return trip. Find the total distance the jogger ran if the total time running was 134 hour.
- Two trains leave the station traveling in opposite directions. One train is 12 miles per hour faster than the other and in 3 hours they are 300 miles apart. Determine the average speed of each train.
- Two trains leave the station traveling in opposite directions. One train is 8 miles per hour faster than the other and in 212 hours they are 230 miles apart. Determine the average speed of each train.
- Answer
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1. The first leg of the trip took 6 hours and the second leg took 2 hours.
3. It took her 12 hour to drive to the airport.
5. 0.5 miles per hour.
7. Airplane: 135 miles per hour; wind: 15 miles per hour
9. 35 hour
11. One train averaged 44 miles per hour and the other averaged 56 miles per hour.