Lesson 3: Modeling Real-World Problems with Equations

Property

Step 1. Locate the 'equals' word(s). Translate to an equal sign.
Step 2. Translate the words to the left of the 'equals' word(s) into an algebraic expression.
Step 3. Translate the words to the right of the 'equals' word(s) into an algebraic expression.

Examples

• 'Five more than $x$ is equal to 26' translates to the equation $x + 5 = 26$. The words 'is equal to' become the $=$ sign.

• 'The difference of $5p$ and $4p$ is 23' translates to $5p - 4p = 23$. The word 'is' becomes the $=$ sign.

Property

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations to solve problems by reasoning about the quantities. This involves assigning a variable to an unknown quantity and translating the problem's context into a mathematical equation.

Examples

• A phone costs 50 dollars more than three times the cost of its case. If the phone costs 350 dollars, what is the cost of the case? Let $c$ be the case's cost. The equation is $3c + 50 = 350$, so $3c = 300$, and $c = 100$. The case costs 100 dollars.
• Sarah has twice as many books as John. Together they have 36 books. How many books does John have? Let $j$ be John's books. The equation is $j + 2j = 36$, so $3j = 36$. John has $j=12$ books.
• A rectangular garden's length is 4 feet longer than its width. If the perimeter is 40 feet, what is the width? Let $w$ be the width. The perimeter is $2w + 2(w+4) = 40$. This simplifies to $4w + 8 = 40$, so $4w = 32$, and $w = 8$ feet.

Explanation

This skill turns a word problem into a solvable math puzzle. You choose a letter to represent the mystery number, then use the clues in the story to build an equation. Solving the equation reveals the answer to the real-world problem.