ALGEBRA PROBLEMS
1. The length of a rectangle is 4 feet less than twice the width of the rectangle. If the perimeter of the rectangle is 85 feet, find the width and the length.
X
L
W x
2W-3
2. A total of $9000 is deposited into two simple interest accounts. In one account the annual simple interest rate is 5%, and in the second account the annual simple interest rate is 7%. The amount of interest earned for 1 year was $485. How much was invested in each account?
3. Running at an average rate of 6 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 3meters per second. The total time for the sprint and the jog back was 4 minutes 6 seconds. Find the length of the track.
4. A plane leaves Paris headed for London at 540 mph. One hour later, a second plane leaves London headed for Paris at 640 mph. If the air route from Paris to London is 2000 miles, how long will it take (after the first plane takes off) for the first plane to pass the second plane?
5. How many liters of water should be evaporated from 200 liters of a 14% saline solution so that the solution that remains is a 22% saline solution?
0
x
.14
x
.22
200x
6. A painter can paint a Bed room in 4 hours. An apprentice can paint the same bed room in 12 hours. If they worked together, how long would it take them to paint the bed room?
7. The sum of the digits of a two-digit number is 11. If we interchange the digits then the new number formed is 45 less than the original. Find the original number.
Let
x = one’s digit t = ten’s digit
x + t = 11 x = 11 – t (equation 1)
Original number = t × 10 + x
Interchanged number = x × 10 + t
Interchanged = Original – 45
x × 10 + t = t × 10 + x – 45
10x + t = 10t + x – 45
10x – x + t = 10t – 45
10x – x = 10t – t – 45
10x– x + 45 = 10t – t
10t – t = 10x – x + 45
10t – t = 10x – x + 45
9t
X
L
W x
2W-3
2. A total of $9000 is deposited into two simple interest accounts. In one account the annual simple interest rate is 5%, and in the second account the annual simple interest rate is 7%. The amount of interest earned for 1 year was $485. How much was invested in each account?
3. Running at an average rate of 6 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 3meters per second. The total time for the sprint and the jog back was 4 minutes 6 seconds. Find the length of the track.
4. A plane leaves Paris headed for London at 540 mph. One hour later, a second plane leaves London headed for Paris at 640 mph. If the air route from Paris to London is 2000 miles, how long will it take (after the first plane takes off) for the first plane to pass the second plane?
5. How many liters of water should be evaporated from 200 liters of a 14% saline solution so that the solution that remains is a 22% saline solution?
0
x
.14
x
.22
200x
6. A painter can paint a Bed room in 4 hours. An apprentice can paint the same bed room in 12 hours. If they worked together, how long would it take them to paint the bed room?
7. The sum of the digits of a two-digit number is 11. If we interchange the digits then the new number formed is 45 less than the original. Find the original number.
Let
x = one’s digit t = ten’s digit
x + t = 11 x = 11 – t (equation 1)
Original number = t × 10 + x
Interchanged number = x × 10 + t
Interchanged = Original – 45
x × 10 + t = t × 10 + x – 45
10x + t = 10t + x – 45
10x – x + t = 10t – 45
10x – x = 10t – t – 45
10x– x + 45 = 10t – t
10t – t = 10x – x + 45
10t – t = 10x – x + 45
9t