# Linear Equation Word Problems

*Step 1*: Read the problem.

*Step 2*: There should be one such quantity which you need to find. Represent that quantity in terms of a variable.

*Step 3*: Relate all other unknown quantities in terms of the variable assumed in step 2.

*Step 4*: Form an equation according to the information in question.

*Step 5*: Solve the equations to find the value of variables.

*Example:* The sum of three consecutive even numbers is 78. What is the smallest of these numbers?

Let us assume that the three consecutive even numbers are *x*, *x* + 2, and *x* + 4.

*x* + *x* + 2 + *x* + 4 = 78

3*x* + 6 = 78

3*x* = 72 implies *x* = 24

*Check your answer*: *x* + (*x* + 2) + (*x* + 4) = 24 + (24 + 2) + (24 + 4) = 24 + 26 + 28 = 78

*Example: *If the difference between two numbers is 38, and the ratio of two numbers is 6:5. Find the numbers.

Let the numbers be x and y.

Then *x* – *y* = 38 … Equation (1)

* x* : *y* = 6 : 5 … Equation (2)

From equation (1), *x *= 38 + *y*

Equation (2) implies => 5*x* = 6*y*

Put *x *= 38 + *y* in 5*x* = 6*y* Þ 5(38 + *y*) = 6y

228 + 5*y* = 6*y* implies *y* = 228

*x* = 38 + 228 = **266**

**The numbers are 228 and 266.**

#### Check Point

- Denise bought a magazine for $2 and some notepads for $3 each. She spent a total of $11. How many notepads did she buy?
- For a field trip 28 students rode in cars and the rest filled six buses. How many students were in each bus if 232 students were on the trip?
- Joe’s bikes rents bikes for $15 plus $8 per hour. Julia paid $47 to rent a bike. For how many hours did she rent the bike?
- Shelly had $24 to spend on five pencils. After buying them, she is left with $14. How much did each pencil cost?
- Ted sold half of his comic books and then bought 15 more. He now has 45. With how many did he begin?

##### Answer key

- 3
- 34
- 4
- $2
- 60

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