# One-Step Equation Word Problems

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One–step equation word problem is a simple word problem involving only addition or subtraction of a constant to an unknown value and either multiplying or dividing a certain number to an unknown quantity.

To solve one-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.

Below are examples illustrating how to solve one-step equation word problem:

1. When 5 is added to a number, the result is 12. What is the number?

Solution:

Let $a$ be the number. The equation is $a+5=12$. Solving for a, we get

$\begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &a+5&=&12\\ &a+5-5&=&12-5 \\ &\therefore a&=&7 \end{array}$

Therefore, the number is 7.

2. If a number is halved, the result is 24. Find the number.

Solution:

Let $n$ be the number. The equation is $\displaystyle \frac{n}{2}=24.$ Solving for $n$, we get

$\begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &\displaystyle \frac{n}{2}&=&24\\ &\left ( 2 \right )\displaystyle \frac{n}{2}&=&24\left ( 2 \right ) \\ &\therefore n&=&48 \end{array}$

Therefore, the number is 48.

3. Mary has $x$ 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: $x+200=230$. Solving for $x$ we get

$\begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &x+200&=&230\\ &x+200-200&=&230-200 \\ &\therefore x&=&30 \end{array}$

Practice Exercises

1. John bought 10 apples at 12 pesos each. How much do 10 apples cost him?
2. If an item is subject to 20% discount, what is the discount if it was originally marked at 500 pesos?
3. If 10 is subtracted from a number, the difference would be 5. What is the number?