MPM2D
Ms. Kueh
Age and Number Problems
Use the problem solving model to solve the following.
1. The sum of 2 numbers is 255. When the smaller is subtracted from the larger, the result is
39. Find the numbers.
2. The sum of 2 numbers is 1584. Their difference is 58. Find the numbers.
3. The sum of 2 numbers is 1211 and their difference is 283. Find the numbers.
4. The mass of an excavator is twice that of a farm tractor. The sum of their masses is 21.9 t.
Find both masses.
5. The sum of 2 numbers is 249. Twice the larger plus 3 times the smaller is 591. Find the
numbers.
6. When 6 times the larger of 2 numbers is added to 7 times the smaller, the result is 114. Ten
times the larger less 9 times the smaller is 66. Find the numbers.
7. Seven times the larger of 2 numbers decreased by 5 times the smaller is 42. Nine times the
larger increased by 8 times the smaller is 186. Find the numbers.
8. Seven times the smaller of 2 numbers plus 9 times the larger is 178. When 10 times the
larger is increased by 11 times the smaller, the result is 230. Find the numbers.
9. Four times the mass of a baseball is 16 g less than the mass of a basketball. The sum of
their masses is 756 g. Find both masses.
10. When the larger of 2 numbers is multiplied by 9 and added to 10 times the smaller, the
result is 389. Seven times the larger diminished by 4 times the smaller is 67. Find the
numbers.
11. The difference in 2 numbers is 92. When the larger is subtracted from 4 times the smaller,
the result is 151. Find the numbers.
12. In one month, a company executive flew round trip twice from London, England to Rome,
Italy. The next month the executive flew one-way to Quebec City, which was 690 km
farther than all the trips of the previous month. How far is it from Rome to London and
from London to Quebec City if the executive flew a total of 6410 km?
13. The sum of 2 numbers is 188. The larger number is 24 more than 3 times the smaller. Find
the numbers.
14. Two numbers have a difference of 123. The larger is 22 more than twice the smaller. Find
the numbers.
15. Two numbers have a difference of 218. The larger is 140 less than twice the smaller. Find
the numbers.
16. The sum of 2 numbers is 46. When 30 is subtracted from 5 times the smaller, the result is 3
times the larger. Find the numbers.
17. The sum of Joan's age and her father's age is 67. Three times Joan's age increased by 7 is
her father's age. How old is Joan?
18. Sal's father is 3 times as old as he is. In six years the sum of their ages will be 68. How old is
Sal?
19. If you double Lucien's age and then subtract 6 you have Peter's age. Two years ago the sum
of their ages was 29. How old is Lucien?
20. Twice Sally's age increased by 3 times Sue's age is 103. Five times Sally's age decreased by 4
times Sue's age is 16. How old will Sally be ten years from now?
21. Pat is 3 times older than her dog. Four years ago, she was 7 times older. How old is Pat's
dog?
22. One-half of Bob's age plus one-third of Terry's age is 24. One-fifth of Bob's age less oneninth of Terry's age is 3. How old is Terry?
23. The sum of the digits of a 2-digit number is 11. The difference between the number and the
number formed by reversing the digits is 27. Find the number.
24. A secret agent, being a mathematician, transmitted an important 2-digit locker number in
the following manner. "The difference in the digits is 4. The sum of the number and the
number formed by reversing the digits is 132." Find the locker number.
25. The sum of the digits of a 2-digit number Is 9. If the number is doubled and then increased
by 18, the result is the number with the digits reversed. Find the number.
Answers
1, 147, 108
4. excavator, 14.6T, tractor 7.3T
7. 16, 14
2. 821, 763
5. 156, 93
8. 12, 10
10. 21, 20
11. 173, 81
12. Rome — London 715 km, London — Quebec City 3550 km
13. 147, 41
14. 224, 101
16. 25, 21
17. 15
19. 13
20. 30
22. 27
23. 74
25. 27
3. 747, 464
6. 12,6
9. baseball 148, basketball
608
15. 576, 358
18. 14
21. The dog is six years old.
24. 84