Linear Equation Word Problems - Pre Algebra

1. A tank holds 200 gallons and drains 15 gallons per minute. After how many minutes does it hold 80 gallons?

   8 minutes. Solve $200 - 15t = 80$: $15t = 120$.

2. Ana is 4 years older than Ben, and their ages add to 30. How old is Ben?

   13. Solve $b + (b + 4) = 30$: $2b = 26$.

3. A rectangle has perimeter 30 and its length is twice its width. What is the width?

   5. Solve $2(2w) + 2w = 30$: $6w = 30$.

4. Half of a number, minus 3, equals 9. What is the number?

   24. Solve $\frac{n}{2} - 3 = 9$: $\frac{n}{2} = 12$.

5. A gym charges 20 dollars to join plus 15 dollars per month. The total paid is 110 dollars. How many months is that?

   6 months. Solve $20 + 15m = 110$: $15m = 90$.

6. A student has 40 dollars and saves 12 dollars per week. After how many weeks will the savings reach 100 dollars?

   5 weeks. Solve $40 + 12w = 100$: $12w = 60$.

7. Three consecutive integers add to 48. What is the smallest?

   15. Solve $n + (n + 1) + (n + 2) = 48$: $3n + 3 = 48$.

8. After solving a word problem equation, what two things should be done with the answer?

   Check it against the original situation, and state it with its units in the context of the problem.

9. A taxi charges 3 dollars plus 2 dollars per mile. A ride costs 19 dollars. How many miles was the ride?

   8 miles. Solve $3 + 2m = 19$: $2m = 16$.

10. Which equation models "5 less than 3 times a number is 16," and what is the number?

    $3n - 5 = 16$, so $n = 7$.

11. Two numbers add to 25, and one is 7 more than the other. What is the smaller number?

    9. Solve $x + (x + 7) = 25$: $2x = 18$.

12. A number doubled, plus 5, equals 17. What is the number?

    6. Solve $2n + 5 = 17$: $2n = 12$.

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