TWO STEP EQUATIONS WORD PROBLEMS

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