Article
Algebra word problems can feel more difficult than ordinary equations because they require you to translate written information into mathematics before solving anything. For students preparing for the ATI TEAS exam, the key is to break the question into smaller parts. Identify what is known, determine what is unknown, and build an equation that represents the relationship described.
1. Identify the unknown value
Start by reading the entire question and deciding what you need to find. Suppose a student buys several notebooks at the same price. The total cost is $24, and each notebook costs $4. How many notebooks did the student purchase? Let \(x\) represent the number of notebooks. Since each notebook costs $4, the total cost is \(4x\). You can write:
2. Recognize common mathematical phrases
Certain words and phrases can suggest mathematical operations. -
- Sum usually indicates addition.
- Difference usually indicates subtraction.
- Product indicates multiplication.
- Quotient indicates division.
- Twice a number means \(2x\).
- Five more than a number means \(x+5\).
- Three less than a number means \(x-3\).
However, do not translate a problem by matching keywords alone. Read the sentence carefully to understand which quantity is being described. For example, “five less than twice a number” means \(2x-5\), not \(2(x-5)\).
3. Build an equation from a real-life situation
Imagine a fitness center charges a registration fee of $15 and $10 per class. A customer pays $65 in total. How many classes did the customer attend? Let \(x\) be the number of classes. The registration fee is fixed, while the class cost is \(10x\). Therefore:
4. Watch for percentages
Some word problems involve percentages. To calculate 15% of $80, convert the percentage into a decimal and multiply: \[ 0.15\times80=12 \] The result is $12. If a question asks for the price after a 15% discount, subtract the discount from the original price: \[ 80-12=68 \] The discounted price is $68 before any applicable taxes or additional fees.
5. Use units to check your answer
Units can help you detect mistakes. If the question asks for the number of classes, your final answer should represent a number of classes, not a dollar amount. Similarly, if you calculate the total cost, the result should be expressed in the appropriate currency. Always return to the original question and confirm that you have answered what was actually asked.
6. Check whether your answer is reasonable
Substitute your solution into the equation or compare it with the original information. For the fitness-center example, five classes at $10 each cost $50. Adding the $15 registration fee gives $65, which matches the stated total. If your answer does not satisfy the original conditions, review your equation and calculations.
Build a reliable problem-solving routine
Practice a few word problems each day. For every question, underline the known values, define the unknown, write an equation, solve it, and check the result. Keep a record of errors, especially mistakes involving word order, negative numbers, percentages, and multiple steps.
