Grade 8 Word Problems: Writing and Solving Linear Equations

Solve each equation and answer the question. Show the steps that isolate the variable.

1. 1.A gym charges a $25 sign-up fee plus $15 per month. The equation 15m + 25 = 145 gives the number of months m for a $145 total. Solve for m.
2. 2.A taxi charges $3.00 plus $2.50 per mile. The equation 2.5x + 3 = 23 models a $23.00 fare. How many miles x was the ride?
3. 3.Two consecutive integers add to 47. The equation x + (x + 1) = 47 models this. What is the smaller integer x?
4. 4.A number is decreased by 3, then the result is multiplied by 4 to give 20. Solve 4(x - 3) = 20.
5. 5.Two phone plans cost the same at x minutes. Solve 5x + 8 = 3x + 20 to find x.
6. 6.A rectangle is 3 cm longer than it is wide, and its perimeter is 26 cm. Solve 2(w + 3) + 2w = 26 for the width w.
7. 7.Solve 2(x + 4) = 3x - 1 to find the number x that makes both expressions equal.
8. 8.A number tripled and then decreased by 7 equals 26. Solve 3x - 7 = 26.
9. 9.Two trucks carry equal loads. Solve 6x - 4 = 2x + 16 to find the load x in tons.
10. 10.Plan A costs $30 plus $0.10 per minute; Plan B costs a flat $50. Solve 0.1x + 30 = 50 for the number of minutes x where the plans cost the same.
11. 11.The temperature falls at a steady rate. Solve -3x + 12 = 3 to find the number of hours x.
12. 12.Solve 7 - 2x = -5 for x.
13. 13.Two angles measuring x and 2x degrees are complementary, so they add to 90. Solve x + 2x = 90.
14. 14.A tank holds 6 liters and is filled at half a liter per minute to reach 14 liters. Solve 0.5x + 6 = 14 for the minutes x.