TWO STEP EQUATIONS WORD PROBLEMS

An equation is a mathematical statement that two expressions have the same value, which are separated by an equal sign, “=”.

  • Distribute to get rid of the parentheses, if necessary.
  • Combine like terms on the same side of the “=”.
  • Add & subtract to get all constants to one side of the “=” and all variables to the other side of the “=”.
  • Multiply & Divide to get the variable by itself.
  • Check using substitution

Example 1 :

The sum of three times a number x and 5 is 17. What is the number?

Solution :

3x + 5 = 17

Subtract 5 on both sides.

3x = 17-5

3x = 12

Divide by 3 on both sides.

x = 12/3

x = 4

Example 2 :

As a membership fee, a health club charges a one-time amount of $40 and charges $25 for each month. The total fee after m months is $240. What is the value of m?

Solution :

40 + 25m = 240

Subtract 40 on both sides.

25m = 240-40

25m = 200

Divide by 25 on both sides.

m = 200/25

m = 8

Example 3 :

A runner warms up for ten minutes and then takes seven minutes to run each mile. The total time after r miles is 45 minutes. How many miles are run? 

Solution :

Time taken for warm up = 10 minutes

Time taken to run each mile = 7 minutes

Number of miles covered = r

10+7r = 45

Subtract 10 on both sides.

7r = 45-10

7r = 35

Divide by 7 on both sides.

r = 35/7

r = 5

Example 4 :

Jaimie picks out a blouse to purchase. It is on sale for 25% off plus she has got $10 off coupon. She pays $23 for the blouse. Determine the original price.

Solution :

Let x be the original price of coupon.

0.75x - 10 = 23

Add 10 on both sides.

0.75x = 23+10

0.75x = 33

Divide by 0.75 on both sides.

x = 33/0.75

x = 44

Example 5 :

Michael is collecting sea glass from the beach. He begins with 14 pieces in his collection and adds 3 new pieces per day. Determine how many days it will take Michael to have 80 pieces of sea glasses in his collection.

Solution :

Let x be the number of days he is collecting sea glass.

Number of glasses collected = 80

14 + 3x = 80

Subtract 14 on both sides.

3x = 80-14

3x = 66

Divide by 3 on both sides.

x = 66/3

x = 22

Example 6 :

Jacob joined a gym last year. His total bill for the year was $410 including a monthly membership fee and a one-time $50 enrollment fee.

Solution :

Let x be Jacob's monthly membership fee.

One time fee = $50.

Total bill = $410

12x + 50 = 410

Subtract 50 on both sides.

12x = 410-50

12x = 360

Divide by 12 on both sides.

x = 360/12

x = 30

Example 7 :

The cell phone company charges $44.95 a month and $0.25 per text message. The bill for the month is $60.45. How many texts (x) were sent?

Solution :

Let x be the number of text messages.

Bill amount = $60.45

Company charge = 44.95

Cost per text message = 0.25

44.95 + 0.25x = 60.45

Subtract 44.95 on both sides.

0.25x = 60.45-44.95

0.25x = 15.5

Divide by 0.25 on both sides.

x = 15.5/0.25

x = 62

Example 8 :

You pay $80 for a game system. The monthly rental fee for games is m dollars. Your cost for the year is $188. Using the equation 12m + 80 = 188, how much is your monthly fee?

a) $8        b) $9        c)  $12       d) $22

Solution :

12m + 80 = 188

Subtracting 80 on both sides

12m = 188 - 80

12m = 108

m = 108/12

m = 9

Monthly rental fee is $9. So, option b is correct.

Example 9 :

You and your friend rent a tandem bike. Your total cost is $42. Write and solve an equation to find the number of extra hours you rented the bike.

solving-two-step-equation-q1

Solution :

Total cost = $42

For three hours, the amount is $24

Let x be the extra number of hours. Charge for extra hours = $4.50

24 + 4.50x = 42

4.50x = 42 - 24

4.50x = 18

x = 18/4.50

x = 4

So, extra hours you rented the bike is 4.

Example 10 :

You and your friend rent a kayak. It costs $40 for the first 4 hours and $7.50 for each extra hour. Your total cost is $62.50. Write and solve an equation to find the number of extra hours you rented the kayak.

Solution :

Total cost = $62.50

For three hours, the amount is $40

Let x be the extra number of hours. Charge for extra hours = $7.50

40 + 7.50x = 62.50

7.50x = 62.50 - 40

7.50x = 22.5

x = 22.5/7.50

x = 3

So, extra hours you rented the kayak is 3.

Example 11 :

Why is the equation 5x − 12 = 23 called a two-step equation?

Solution :

Given equation is 5x − 12 = 23

Step 1 :

To solve this equation, we have to add 12 on both sides

5x = 23 + 12

5x = 35

Step 2 :

Dividing by 5 on both sides

x = 35/5

x = 7

Example 12 :

Describe and correct the error in solving the equation.

solving-two-step-equation-q2.png

Solution :

Solving this equation,

4 = (y/8) + 1

Subtracting 1 on both sides

4 - 1 =(y/8)

3 = (y/8)

Multiplying by 8, we get

3(8) = y

y = 24

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