Solving Word Problems on the SAT

This guide explains effective strategies for breaking down and solving SAT math word problems. The focus is on clear methods that help you translate real-world scenarios into mathematical expressions, set up equations correctly, and check your work. Use these techniques to approach word problems confidently and efficiently.

Overview

Word problems on the SAT test your ability to convert everyday situations into math problems. They often require multiple steps, careful reading, and logical reasoning. Common types of word problems include:

• Linear equations and systems of equations
• Ratios, proportions, and percentages
• Distance, rate, and time problems
• Work and mixture problems
• Geometry-based scenarios

Understanding these categories and practicing problem-solving techniques can improve accuracy and boost your score.

Strategies for Solving Word Problems

1. Active Reading

Use the "CUBE" strategy to organize information:

• Circle numerical values and units.
• Underline key information and relationships.
• Box the specific question being asked.
• Eliminate irrelevant details.

This method helps ensure that you capture the essential information needed to form an equation.

2. Translate Words into Equations

Familiarize yourself with common phrases:

• "Sum" or "increased by" → addition
• "Difference" or "less than" → subtraction
• "Product" or "times" → multiplication
• "Quotient" or "per" → division

For example, the phrase "Five more than twice a number is 17" translates to the equation: $2x + 5 = 17$

3. Define Variables Clearly

Assign variables to unknown quantities and maintain consistency throughout the problem. Clear definitions help in setting up and solving the equations accurately.

4. Draw Diagrams

A diagram or sketch can simplify complex problems, especially those involving geometry or movement. Visual representations can help in tracking relationships among variables.

5. Check Units and Answer Requirements

Ensure that your final answer is in the correct units and meets the specific requirements of the question. This step helps catch any discrepancies that may arise from misinterpretation.

Practice Problems

Problem 1: Sales Tax Calculation

Question:
Alex buys a pair of shoes. The sales tax rate in his town is 6%. The total price, including tax, is $115.54. How much did the shoes cost before tax?

Solution:
Let $x$ be the pre-tax cost. The equation becomes:
$x + 0.06x = 115.54$
This can be simplified to:
$1.06x = 115.54$
Solve for $x$ by dividing both sides by 1.06:
$x = \frac{115.54}{1.06} \approx 109.00$

Answer:
The shoes cost approximately $109.00 before tax.

Problem 2: System of Equations

Question:
Luca buys apples at $2 each and bananas at $3 each. He buys twice as many bananas as apples and spends $48. How many bananas did he buy?

Solution:
Let $a$ be the number of apples. Then, the number of bananas is $2a$. The total cost can be expressed as:
$2a + 3(2a) = 48$
Simplify the equation:
$2a + 6a = 48$
$8a = 48$
Divide both sides by 8:
$a = 6$
Thus, the number of bananas is:
$2a = 12$

Answer:
Luca bought 12 bananas.

Problem 3: Compound Interest

Question:
You invest $5,000 in an account with a 3% annual interest rate, compounded annually. How much will you have after 5 years?

Solution:
Use the compound interest formula:
$A = P(1 + r)^t$
Where:

• $P = 5000$,
• $r = 0.03$, and
• $t = 5$.

Substitute the values:
$A = 5000(1 + 0.03)^5$
Calculate:
$A \approx 5000(1.15927) \approx 5796.35$

Answer:
You will have approximately $5,796.35 after 5 years.

Video Resource

For a visual walkthrough on solving SAT word problems, watch the following instructional video:

Additional Resources

Enhance your study with these valuable resources:

• SAT Sphere CourseSAT Sphere Course – A comprehensive digital course with built-in lessons, practice questions, exams, and everything you need for the Digital SAT.
• Strategies for SAT Word ProblemsStrategies for SAT Word Problems (additional resource placeholder)
• SAT Word Problem TechniquesSAT Word Problem Techniques (additional resource placeholder)

Conclusion

Solving word problems on the SAT involves careful reading, translating scenarios into equations, defining variables clearly, and checking for accuracy in units and answers. With regular practice and the strategies outlined in this guide, you'll build the skills needed to tackle SAT word problems confidently and efficiently.