1. Real World Problems
Integer Coefficients

2. Problem 1
Three added to eight times a number is the same as three times the value of two times the number minus one. What is the number?

3. Problem 2
Ten less than 3 times a number is the same as the number plus 4.

4. Problem 3
Six times a number plus 4 is the same as the number minus 11.

5. Problem 4
Fifteen more than twice the hours Carla worked last week is the same as three times the hours she worked this week decreased by 15. She worked the same number of hours each week. How many hours did she work each week?

6. Problem 5
Twelve decreased by twice a number is the same as eight times the sum of the number and 4. What is the number?

7. Problem 6
Company A offers a starting salary of $28,000 with a raise of $3,000 each year. Company B offers a starting salary of $36,000 with a raise of $2,000 per year. Company C offers a starting salary of $18,000. After how many years would the salaries for Companies A and B be the same? How much of a raise per year would Company C have to offer to equal the salaries of Companies A and B in the year in which the salaries of those two are the same?

8. Problem 1 - Answers
3 + 8n = 3(2n - 1); n = -3

9. Problem 2 - Answers
3n - 10 = n + 4; n = 7

10. Problem 3 – Answers
6n + 4 = n - 11; n = -3

11. Problem 4 – Answers
15 + 2h = 3h - 15; h = 30

12. Problem 5 – Answers
12 - 2n = 8(n + 4); n = -2

13. Problem 6 – Answers
28, ,000n = 36, ,000n; n = 8; Company C would need to give a raise of $4,250 per year to equal the salaries of Companies A and B, $52,000, after year 8.