Lesson 4: Word Problems

Property

To solve word problems with two unknown quantities, translate the sentences into a system of linear equations. Follow this problem-solving strategy:
Step 1. Read the problem. Make sure all the words and ideas are understood.
Step 2. Identify what we are looking for.
Step 3. Name what we are looking for. Choose variables to represent those quantities.
Step 4. Translate into a system of equations.
Step 5. Solve the system of equations using good algebra techniques.
Step 6. Check the answer in the problem and make sure it makes sense.
Step 7. Answer the question with a complete sentence.

Examples

• The sum of two numbers is 25. One number is 5 more than the other. Find them. Let the numbers be $x$ and $y$. The system is $\begin{cases} x+y=25 \\ x=y+5 \end{cases}$. Substituting gives $(y+5)+y=25$, so $2y=20$ and $y=10$. Then $x=10+5=15$. The numbers are 10 and 15.

• The perimeter of a rectangle is 40 inches. The length is 4 inches less than twice the width. Find the dimensions. Let $L$ be length and $W$ be width. The system is $\begin{cases} 2L+2W=40 \\ L=2W-4 \end{cases}$. Substituting gives $2(2W-4)+2W=40$, so $6W-8=40$, $6W=48$, and $W=8$. Then $L=2(8)-4=12$. The length is 12 inches and the width is 8 inches.