Number Problems

NUMBER PROBLEMS: 1. When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. Find the number.

2. When 7 times a number is decreased by 8, the answer is the same as when 3 times the number is increased by 4. Find the number.

3. Eight times a number increased by 9 is the same as 15 more than 7 times the number. Find the number.

4. Thirty decreased by 6 times a number is the same as 16 more than the number. Find the number.

5. When 6 times a number is increased by 11 the result is 16 less than 9 times the number. Find the number.

6. A piece of fabric 180 inches long is cut into two pieces such that 3 times the larger piece exceeds 4 times the smaller piece by 85 inches. How large are the two pieces of fabric?

GENERAL PROBLEMS: 1. A repair bill on a sailboat came to $1603, including $532 for parts and the remainder for labor. If the cost of labor is $63 per hour, how many hours of labor did it take to repair the sailboat?

2. Rent-A-Heap car rental company charges $125 plus $0.20 per mile to rent one of their cars. Suppose you are limited to $335. How many miles can you drive the car?

3. The perimeter of a rectangle is 30 inches. If the length is one inch longer than the width, find the dimensions of the rectangle.

4. An elevator at a construction site carries a 2800 pound load. If the elevator operator weighs 265 pounds and each cement bag weighs 95 pounds, how many bags of cement are safely lifted on the elevator in this trip?

5. The perimeter of a rectangle is 126 feet. If the length is twice the width, find the dimensions of the rectangle.

6. A company manufactures and sells blank CDs. The weekly fixed cost is $10,000 and it cost $4.00 to produce each CD. How many CDs must be produced and sold each week for $10,580?

7. A salesperson earns $300 per week plus 5% commission of sales. How much must be sold to earn $800 in a week? BREAK-EVEN PROBLEMS: 1. You are choosing between two health clubs. Club A offers membership for a fee of $40 plus a monthly fee of $25. Club B offers membership for a fee of $15 plus a monthly fee of $30. After how many months will the total cost at each health club be the same?

2. Video Store A charges $9 to rent a video game for one week. There is no membership fee. Video Store B charges a one time membership fee of $50 plus $4 to rent a video game for one week. After how many video-game rentals will the total amount spent at each store be the same?

3. In 2005, there were 13,300 students at college A, with a projected enrollment increase of 1000 students per year. In the same year at college B, there were 26,800 students with a projected enrollment decline of 500 students per year. a) According to these projections, when will the colleges have the same enrollment? b) What will be the enrollment in each college at that time?

4. A tennis club offers two payment options. Members can pay a monthly fee of $30 plus $5 per hour for court rental time. The second option has no monthly fee, but court time costs $7.50 per hour. After how many hours will the two options cost the same? CONSECUTIVE INTEGER PROBLEMS: 1. Find two consecutive integers whose sum is 123.

2. Find two consecutive integers whose sum is -97.

3. Find two consecutive even integers whose sum is−38.

4. Find three consecutive even integers whose sum is 8.

5. Find two consecutive odd integers whose sum is −36.

6. Find three consecutive odd integers whose sum is 75.