Math 100
Word Problems Involving Numbers
Use a separate piece of paper
Set 1
Write a variable equation and solve (don’t need to use the 4 step process).
1. The sum of a number and 4 is 10.
2. The product of 5 and a number is 45.
3. The difference between a number and –7 is 12.
4. Three decreased by four times a number is 15.
5. The difference between three times a number and one is 2.
6. Five less than six times a number is 37.
7. One more than three times a number is -8.
8. Twice a number, increased by three is 27.
9. Seven less than three times a number is –52.
10. Two increased by five times a number is 32.
Use the figure and the information below it to write an equation involving x.
Find the lengths of all sides.
11.
12.
x
8
7
x
6
x
Perimeter = 26
x
x
x
Perimeter = 29
9
Perimeter = 24
14.
13.
15.
6
4
Perimeter = 12
8
x
3
16.
x
8
Area = 40
8
x
Area = ½ bh = 40
Consecutive Integer Problems (use the 4 step process):
17. Find two consecutive integers whose sum is –45.
18. Two pages that face each other in a book have 569 as the sum of their page numbers.
What are the page numbers?
19. Find two consecutive odd integers whose sum is 68.
20. Find two consecutive even integers such that six times the smaller added to the larger
gives a sum of 86.
Set 2
Solve the following problems on a separate sheet of paper
Use the four step process
1. Define variables
2. Set up an equation
3. Solve the equation
4. Answer the question
1. One number is 10 more than another number. Their sum is 28. Find both numbers.
2. One number is 6 less than another number. Their sum is 52. Find both numbers.
3. The sum of two numbers is 82. One number is 12 less than another number. Find
both numbers.
4. One number is 20 more than another number. Their sum is 102. Find both numbers.
5. The sum of two numbers is 42. One number is 6 more than two times another
number. Find both numbers.
6. One number is 14 less than three times another number. Find both numbers if the
sum of the two numbers is 34.
7. The sum of two numbers is 34. One number is 8 less than twice another number.
Find both numbers
8. The sum of two numbers is 46. One number is 8 less than twice another number.
Find both numbers.
9. One number is three times another number. Find both numbers if the sum of the two
numbers is 84.
10. One number is 4 less than three times another number. Find both numbers if the sum
of the two numbers is 56.
11. One number is 5 more than three times another number. Find both numbers if the
sum of the two numbers is 37.
12. Find three numbers whose sum is 29 if then second number is 2 more than the first
number and the third number is 12 more than the first number.
13. Find three numbers whose sum is 52 if the second number is 6 less than the first
number and the third number is 16 more than the first number.
14. Find three numbers whose sum is 70 if the second number is 2 less than the first
number and the third number is 8 less than twice the first number.
15. Seventy-Two decreased by twice a number is 30. Find the number
16. George is 4 cm taller than John. The sum of the heights is 405 cm. How tall is
George?
17. Carla has twice as much money as Peter. Together they have $105. How much does
Carla have?
18. A ribbon 9 feet long is cut into two pieces. One piece is 1 foot longer than the other.
What are the lengths of the pieces?
Set 1 Answers
1. x + 4 = 10
4. 3 – 4x = 15
7. 3x + 1 = -8
10. 2 + 5x = 32
13. x = 5
16. x = 10
19. 33, 35
Set 2 Answers:
1.
9,19
3.
47, 35
5.
12, 30
7.
14, 20
9.
21, 63
11.
8, 29
13.
14, 8, 30
15.
x = 21
17.
$70
3. x – (-7) = 12
6. 6x - 5 = 37
9. 3x – 7 = -52
12. x = 11
15. x = 5
18. 284, 285
2. 5x =45
5. 3x – 11 = 2
8. 2x + 3 = 27
11. x = 7
14. x = 7
17. –22, -23
20. 12, 14
2.
4.
6.
8.
10.
12.
14.
16.
18.
29, 23
41, 61
12, 22
18, 28
15, 41
5, 7, 17
20, 18, 32
204 ½ cm
4ft and 5ft