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### Two-Step Equation Word Problems Worksheets

Two–step equation word problem is a simple word problem involving both multiplying a certain factor to the unknown variable or quantity and either addition or subtraction of a constant to this product. To solve two-step equation word problems, follow the following steps:

1. Assign a variable for the unknown quantity or number.
2. Set up the equation that best translate the word problem.
3. Solve the defining equation.
4. State the final answer.
Below are examples illustrating how to solve one-step equation word problem:

1. When 5 is added to twice a number, the result is 13. What is the number?

Solution:

Let $$a$$ be the number. The equation is $$2a+5=13$$. Solving for $$a$$ we get
$\begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &2a+5&=&13\\ &2a+5-5&=&13-5 \\&2a&=&8\\ &\therefore a&=&4 \end{array}$
Therefore, the number is 4.

2. If 3 is subtracted from half a number, the result is 24. Find the number.

Solution:

Let $$n$$ be the number. The equation is $$\displaystyle \frac{n}{2}-3=24$$. Solving for $$n$$ we get
$\begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &\displaystyle \frac{n}{2}-3&=&24\\ &\displaystyle \frac{n}{2}&=&21 \\ &\therefore n&=&42 \end{array}$
Therefore, the number is 42.

3. Mary has $$3x$$ pesos in her wallet. If her mother would give her additional 200 pesos, she will have 230 pesos in all. How much money does she originally have?

Solution:

Since the unknown amount is already as $$x$$, so the equation is $$3x+200=230$$. Solving for $$x$$ we get
$\begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &3x+200&=&230 \\ &3x&=&30&\textup{subtract 200 to both sides of the equation} \\ &\therefore x&=&10&\textup{divide both sides by 3} \end{array}$
Therefore, Mary originally has P10 in her wallet.

Practice Exercises

Practice Exercises
1. If an item is subject to 20% discount, what is the selling price if it was originally marked at 500 pesos?
2. If 10 is subtracted from three times number, the difference would be 5. What is the number?
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