# 5.4E: Exercises

- Page ID
- 30526

**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**-
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**-
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 \(\frac{1}{2}\) 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 \(1 \frac{1}{2}\) 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 \(1 \frac{1}{4}\) hours. Returning upstream against the current, the boat can only travel \(8 \frac{3}{4}\) 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 \(1 \frac{3}{4}\) 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 \(2 \frac{1}{2}\) hours they are \(230\) miles apart. Determine the average speed of each train.

**Answer**-
1. The first leg of the trip took \(6\) hours and the second leg took \(2\) hours.

3. It took her \(\frac{1}{2}\) hour to drive to the airport.

5. \(0.5\) miles per hour.

7. Airplane: \(135\) miles per hour; wind: \(15\) miles per hour

9. \(\frac{3}{5}\) hour

11. One train averaged \(44\) miles per hour and the other averaged \(56\) miles per hour.