Algebra- Basic Word Problems: Equations

Question 1

The sum of twice a number and 7 is 15. What is the number?

Answer 1

x = 4 (2x + 7 = 15 -> 2x = 8)

Question 2

5 less than three times a number is 10. Find the number.

Answer 2

x = 5 (3x - 5 = 10 -> 3x = 15)

Question 3

A number divided by 4, plus 3, equals 8. What is the number?

Answer 3

x = 20 (x/4 + 3 = 8 -> x/4 = 5)

Question 4

The product of a number and 6 is equal to the number plus 25.

Answer 4

x = 5 (6x = x + 25 -> 5x = 25)

Question 5

10 more than a number is twice the number. Find the number.

Answer 5

x = 10 (x + 10 = 2x)

Question 6

Two consecutive integers have a sum of 31. What are they?

Answer 6

15 and 16 (x + (x+1) = 31 -> 2x = 30)

Question 7

Three times the sum of a number and 4 is 21.

Answer 7

x = 3 (3(x + 4) = 21 -> x + 4 = 7)

Question 8

A number decreased by 12 is one-third of itself.

Answer 8

x = 18 (x - 12 = x/3 -> 3x - 36 = x -> 2x = 36)

Question 9

The difference between four times a number and 6 is 18.

Answer 9

x = 6 (4x - 6 = 18 -> 4x = 24)

Question 10

Half of a number is 8 more than one-fourth of the number.

Answer 10

x = 32 (x/2 = x/4 + 8 -> 2x = x + 32)

Question 11

7 more than the quotient of a number and 5 is 10.

Answer 11

x = 15 (x/5 + 7 = 10 -> x/5 = 3)

Question 12

The sum of three consecutive integers is 45. Find the smallest one.

Answer 12

14 (x + (x+1) + (x+2) = 45 -> 3x + 3 = 45)

Question 13

4 times a number is the same as the number added to 12.

Answer 13

x = 4 (4x = x + 12 -> 3x = 12)

Question 14

8 subtracted from a number is equal to 20.

Answer 14

x = 28 (x - 8 = 20)

Question 15

15 is 3 more than twice a number.

Answer 15

x = 6 (15 = 2x + 3 -> 12 = 2x)

Question 16

A number increased by 20% of itself is 60.

Answer 16

x = 50 (1.20x = 60 -> x = 50)

Question 17

Perimeter of a rectangle is 24. Length is twice the width. Find width.

Answer 17

w = 4 (2(w + 2w) = 24 -> 6w = 24)

Question 18

A 20ft board is cut into two pieces. One is 4ft longer than the other.

Answer 18

8ft and 12ft (x + (x+4) = 20 -> 2x = 16)

Question 19

Adding 9 to a number is the same as tripling the number.

Answer 19

x = 4.5 (x + 9 = 3x -> 9 = 2x)

Question 20

One number is 5 more than another. Their sum is 13.

Answer 20

4 and 9 (x + (x+5) = 13 -> 2x = 8)

Question 21

The ratio of two numbers is 2:3. Their sum is 20.

Answer 21

8 and 12 (2x + 3x = 20 -> 5x = 20)

Question 22

6 times the difference of a number and 2 is 18.

Answer 22

x = 5 (6(x - 2) = 18 -> x - 2 = 3)

Question 23

A number divided by 2 is 5 less than the number.

Answer 23

x = 10 (x/2 = x - 5 -> x = 2x - 10)

Question 24

25% of a number is 40. What is the number?

Answer 24

x = 160 (0.25x = 40 -> x = 160)

Question 25

The sum of two consecutive even integers is 26.

Answer 25

12 and 14 (x + (x+2) = 26 -> 2x = 24)

Question 26

14 is 4 less than three-fifths of a number.

Answer 26

x = 30 (14 = 3/5x - 4 -> 18 = 3/5x -> 90 = 3x)

Question 27

A father is 3 times as old as his son. Sum of ages is 48.

Answer 27

Son is 12, Father is 36 (s + 3s = 48 -> 4s = 48)

Question 28

A number plus its double and its triple is 60.

Answer 28

x = 10 (x + 2x + 3x = 60 -> 6x = 60)

Question 29

Price was reduced by $5 and is now $12. Original price?

Answer 29

$17 (x - 5 = 12)

Question 30

40 is 10 less than half of a number.

Answer 30

x = 100 (40 = x/2 - 10 -> 50 = x/2)

Question 31

Subtracting 7 from a number gives 14.

Answer 31

x = 21 (x - 7 = 14)

Question 32

2 more than 4 times a number is 26.

Answer 32

x = 6 (4x + 2 = 26)

Question 33

Dividing a number by 3 gives 9.

Answer 33

x = 27 (x/3 = 9)

Question 34

The square of a number is 64.

Answer 34

x = 8 (or -8)

Question 35

30 is 5 times the sum of a number and 2.

Answer 35

x = 4 (30 = 5(x + 2) -> 6 = x + 2)

Question 36

A number is 6 more than its opposite.

Answer 36

x = 3 (x = -x + 6 -> 2x = 6)

Question 37

10 times a number minus 8 is 72.

Answer 37

x = 8 (10x = 80)

Question 38

One-fifth of a number is 12.

Answer 38

x = 60 (x/5 = 12)

Question 39

Twice the difference of 10 and a number is 4.

Answer 39

x = 8 (2(10 - x) = 4 -> 10 - x = 2)

Question 40

The sum of a number and its half is 15.

Answer 40

x = 10 (x + 0.5x = 15 -> 1.5x = 15)