SOLVING ONE STEP EQUATIONS WORD PROBLEMS

Example 1 :

Eighteen more than the number n is 125. What is the value of n?

Solution :

Eighteen more than the number n = 125

18 + n = 125

Subtract 18 on both sides.

n = 125-18

n = 107

Example 2 :

Jim’s three fish tanks contain an equal amount of fish. If Jim has a total of 27 fish, how many fish are in each tank?

Solution :

Number of fish tank Jim has = 3

Let x be the number of fishes in each tank.

Total number of fishes = 24

3x = 27

Divide by 3 on both sides

x = 27/3

x = 9

Example 3 :

Steven went to the store and bought five sweatshirts. He spent $45. What was the price of each shirt?

Solution :

Number of sweat shirts he bought = 5

Let x be the cost of each sweat shirt.

Cost spent = $45

5x = 45

Divide by 5 on both sides.

x = 45/5

x = 9

Example 4 :

How many boxes of envelopes can you buy with $12, if one box costs $3?

Solution :

Let x be the number of boxes.

Cost of one box = $3

Cost spent = $12

3x = 12

Divide by 3 on both sides.

x = 12/3

x = 4

Example 5 :

At a restaurant, Bill and his four friends decided to divide the bill evenly. If each person paid $12, what was the total bill?

Solution :

Bill + his four friends = 5 persons

Each friend is paying = $12

Total bill = 5(12)

= $60

Example 6 :

Last Saturday, Allyson had $38. For her birthday she received more money. She now has $90. How much money did she receive?

Solution :

Let x be the amount she has received.

The amount that she has = $90

x + 38 = $90

Subtract 38 on both sides.

x = 90 - 38

x = $52

So, he has received $52.

Example 7 :

The sum of three fourths of the number a and 24 is negative 9. What is the value of a?

Solution :

(3/4) of a + 24 = -9

3a/4 + 24 = -9

3a/4 = -9-24

3a/4 = -33

Multiply by 4 on both sides.

3a = -33(4)

Divide by 3 on both sides, we get

a = -11(4)

a = -44

Example 8 :

Twenty is 7 less than twice the number w. What is the value of w?

Solution :

Twice the number w = 2w

20 = 2w-7

Add 7 on both sides.

20+7 = 2w

2w = 27

Divide by 2 on both sides, we get

w = 27/2

w = 13.5

Example 9 :

-11+ x = 9

Given the above equation, what is the value of 20-(11-x) ?

Solution :

-11+ x = 9

Add 11 on both sides

x = 9 + 11

x = 20

20-(11-x) :

By applying the value of x in the given expression.

= 20 - (11 - 20)

= 20 - (-9)

= 20+9

= 29

Example 10 :

Two and three fifths of a number equals -26. What is the number?

Solution :

Let x be the required number.

2  3/5 of x = -26

13/5 of x = -26

13x/5 = -26

Multiply by 5 on both sides, we get

13x = -26(5)

Divide by 13 on both sides.

x = -26(5)/13

x = -2(5)

x = -10

Example 11 :

Number a is increased by the product of b and c. The result is divided by c and then
decreased by b. Finally, that result is multiplied by c. Which of the following is the final result?

a)  a       b)  a + bc - b     c)  (a/c) + b - c      d)  (a/c) + b - bc

Solution :

Number a is increased by the product of b and c :

= a + bc

The result is divided by c,

= a/c + (bc/c)

= (a/c) + b

Decreased by b,

= (a/c) + b - b

= a/c

Multiplied by c,

= c(a/c)

= a

So, option a is correct.

Example 12 :

For which of the following number of sides will the measure of an angle be 144 degrees?

a) 6      b) 8      c) 10      d) 12

Solution :

• Sum of interior angles of polygon = (n - 2) 180
• Each interior angle of n sided polygon = (n - 2) 180 / n

When n = 6

= (6 - 2) 180 / 6

= 4(180)/6

= 4(30)

= 120

So, option a is not correct.

When n = 8

= (8 - 2) 180 / 8

= 6(180)/8

= 135

So, option b is not correct.

When n = 10

= (10 - 2) 180 / 10

= 8(180)/10

= 144

So, option c is correct.