Word Problems

1. The sum of two numbers is 54. If the larger is divided by the smaller, the quotient is 2 and the remainder is 3. Find the numbers.

2. The denominator of a fraction is 4 less than the numerator. If the denominator is doubled and the numerator is increased by 6, the sum of the original fraction and the new one is 3. Find the original fraction.

3. A man has ₱ 45,000 invested parts at 2% and the remainder at 3% simple interest. How much is invested at each rate if the total annual income from these investments is ₱ 1,100?

4. A man has ₱ 20,000 invested at 7% and ₱ 50,000 at 4% simple interest. What additional amount must he invest at 6% to give him an overall return of 5%?

5. A man invests ₱ 4,000 at one interest rate and ₱ 5,000 at 1% greater rate. Find the income for each investment if the total annual income from these investments is ₱ 410.

6. Admission tickets to a theater were ₱ 60 for adults and ₱ 25 for children receipts for the day showed that 280 persons attended and ₱ 14,000 was collected. How many children attended that day?

7. How many quarts of pure alcohol must be added to 10 quarts of 10% alcohol solution to obtain a mixture which is 25% alcohol?

8. Two motorists start toward each other at 4:30 P.M from towns 250 miles apart. If their respective average speeds are 20mi/hr and 30mi/hr, at what time will they meet?

9. One clerk can file 12 folders per minute and second clerk 9 folders per minute. How long will it take them working together to file 672 folders?

10.Fred is three times older than his sister Mary. Four years ago he was five times as old as his sister. Find their present ages.

11.Separate 27 into two parts whose product is 92. Find the numbers.12.A picture 8 in. by 12 in. is placed in a frame which has uniform width. If the area

of the frame equals the area of the picture, find the width of the frame.13.The tens digit of a certain number is 4 more than the units digit. The sum of the

squares of the two digits is 26. Find the number.14. A grocer bought a number of items for ₱ 1,140. Later the price increased at ₱ 2

per item and as a result he received 24 fewer items for the same amount of money. How many items were in his first purchase?

15. An airplane flew 660 miles with the wind, and then took 40 minutes longer for the return flight against the wind. If the plane flies 200 miles per hour in still air, find the speed of the wind.