Word Problems 1. Find the values of five consecutive odd integers whose sum is 355. 2. If you add one inch to each side of a square, you get a new square whose area is 15 square units more than the original. What is the perimeter of the original square? 3. Find three consecutive odd numbers whose sum is the square of the second odd number. 4. A certain two-digit number has the sum of its digits equal to 13. If its digits are reversed, the new num- ber is 27 larger than the original. Find the original number. 5. A certain three-digit number has the sum of its dig- its equal to 18. If its tens and units digits are inter- changed, the number is increased by 36. If its hun- dreds and units digits are interchanged, the number is reduced by 99. Find the original number. 6. The numerator of a positive fraction is 5 more than thrice its denominator. If 13 is added to the de- nominator and 9 is subtracted from the numerator, the resulting fraction is twice the reciprocal of the original number. Find the original fraction. 7. The area of a rectangle is 16 square centimeters. If the length were increased by 3 centimeters and the width decreased by 3 centimeters, the area will in- crease by 9 square centimeters. Find the original dimensions of the rectangle. 8. A group of friends decided to rent a room in a re- sort. To cover the rent expenses, each has to con- tribute 111 pesos each. However, two of the ex- pected “friends” decided not to go at the last minute and so the share for each person became 185 pesos each. How many friends were there originally? 9. Cleverlyn and Junnifer leave the same place at the same time to go back to their respective houses. Cleverlyn’s house is 1500 meters away, while Jun- nifer’s house is 2500 meters away. Fortunately, Jun- nifer’s speed is 10 meters per minute faster than Cleverlyn’s and so they arrive at their houses at the same time. How long did they walk? 10. Diophantus’s youth lasted 1 6 of his life. He grew a beard after 1 12 more of his life. After 1 7 more of his life, Diophantus married. Five years later, he had a son. The son lived exactly half as long as his father and Diophantus died just four years after his son’s death. How long did Diophantus live? 11. You are arranged in line by class number (with class number 1 in front) and a friend directly in front of you tells you that the difference between twice his class number and the class number of the person behind you is 42. What is your class number?
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- Integers, Numerical digit, Summation, Kanye West, Jay-Z, Mathematics in medieval Islam