Lesson Objectives
• Demonstrate an understanding of how to solve a Linear Equation in One Variable
• Learn the six-step process for solving any word problem that involves a Linear Equation in One Variable
• Learn how to check the solution for a word problem
• Learn how to set up and solve age word problems

## How to Solve Age Word Problems

Over the course of the last few lessons, we have learned how to solve a linear equation in one variable. In real life, our problems will not be given to us in such a manner. We will need to create an equation based on the context of the given situation. When we first learn how to set up and solve word problems, it can be a real challenge for many students. It is often helpful to follow a step by step method for solving word problems.

### Six-step method for Applications of Linear Equations in One Variable

1. Read the problem carefully and determine what you are asked to find
• Write down the main objective of the problem
2. Assign a variable to represent the unknown
• If more than one unknown exists, we express the other unknowns in terms of this variable
3. Write out an equation which describes the given situation
4. Solve the equation
5. State the answer using a nice clear sentence
6. Check the result by reading back through the problem
• We need to make sure the answer is reasonable. In other words, if asked how many miles were driven to the store, the answer shouldn't be (-3) as we can't drive a negative amount of miles.

### Age Word Problems

Age word problems are very common in our study of algebra. This type of word problem generally gives the sum of the ages of family members or friends and asks us to determine the individual ages. Let's take a look at an example.
Example 1: Solve each word problem
Two siblings, Jamie and Steven have a combined age of 15. Steven is twice the age of Jamie. Find the age of each sibling.
1. Read the problem carefully and determine what you are asked to find
• We are asked to find the age of each sibling.
2. Assign a variable to represent the unknown
• Let x = Jamie's age
• Then 2x = Steven's age (since it's twice the age of Jamie)
3. Write out an equation which describes the given situation
• If we add Jamie's age (x) with Steven's age (2x), the result is 15.
• x + 2x = 15
4. Solve the equation
• x + 2x = 15
• 3x = 15
• 3/3 x = 15/3
• x = 5
5. State the answer using a nice clear sentence
• Since x represents Jamie's age, we know that Jamie is 5 years old.
• Since 2x represents Steven's age, we know that Steven is 2 • 5 or 10 years old
• Jamie is 5 years old and Steven is 10 years old.
6. Check the result by reading back through the problem
• We know that the sum of their ages is 15.
• Check: 5 + 10 = 15
• 15 = 15
• We know that Steven is twice the age of Jamie
• Check: 2 • 5 = 10
• 10 = 10
• Since both of our checks were true, we can say our answer is correct.

#### Skills Check:

Example #1

Solve each word problem.

Two sisters, Mary and Claudia have a combined age of 24. 6 years ago, Claudia was the same age as Mary is today. How old is each girl?

A
Mary:13, Claudia:11
B
Mary:14, Claudia:10
C
Mary:9, Claudia:15
D
Mary:15, Claudia:9
E
Mary:10, Claudia:14

Example #2

Solve each word problem.

In 4 years, Molly and Emma will have a combined age of 44. Molly is 5 times as old as Emma. How old is each girl?

A
Molly:25, Emma:5
B
Molly:20, Emma:4
C
Molly:3, Emma:15
D
Molly:30, Emma:6
E
Molly:24, Emma:19

Example #3

Solve each word problem.

Jenna, Carly, and Holly all attend the same church. The church is holding a fair and all attendees must be at least 15 years of age. The sum of their ages is 39. Additionally, Jenna is 4 years younger than Carly, but double the age of Holly. Which girl(s) can’t attend the fair?

A
Jenna
B
Carly
C
Carly, Holly
D
Jenna, Holly
E
Holly         