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SAT Math skill page

SAT Systems Word Problems Practice

Turn totals, rates, and comparisons into two equations before solving.

Practice systems word problems in Dolphin SAT Try examples
12-18 min practice time 3 examples on page Algebra
Practice time 12-18 min
On-page examples 3 examples
Best for Algebra

What this tests

What to know for this SAT skill

Practice examples

Try a few SAT-style questions

Example 1 Easy

Tickets cost $5 for students and $8 for adults. Which expression represents the total cost for s student tickets and a adult tickets?

  1. 5s + 8a
  2. 8s + 5a
  3. 13sa
  4. 5a + 8s
Show answer and explanation

Answer: 5s + 8a

Multiply each ticket type by its price and add the totals.

Example 2 Medium

A total of 20 tickets were sold. Student tickets cost $5, adult tickets cost $8, and total revenue was $124. How many adult tickets were sold?

  1. 6
  2. 8
  3. 10
  4. 12
Show answer and explanation

Answer: 8

Let a be adult tickets and s be student tickets. s + a = 20 and 5s + 8a = 124. Substituting s = 20 - a gives 100 + 3a = 124, so a = 8.

Example 3 Hard

Two numbers have sum 31. One number is 4 more than twice the other. What is the larger number?

  1. 9
  2. 17
  3. 22
  4. 26
Show answer and explanation

Answer: 22

Let the smaller number be x. The larger is 2x + 4, so x + 2x + 4 = 31. Then 3x = 27, x = 9, and the larger number is 22.

Quick drills

Practice this skill from more angles

Drill 1

Define variables from a word problem

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 2

Create two equations from totals and constraints

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 3

Solve systems by substitution or elimination

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 4

Interpret the solution in context

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Avoid these traps

Common mistakes on this skill

Solving before naming the task

The SAT often hides the real skill inside familiar wording. Identify the rule, relationship, or question type first.

Choosing an answer that only partly fits

Many wrong answers are close. Check every condition in the question before committing.

Skipping the final check

Reread what the question asks for so you do not answer a nearby but different question.

Study plan

How to practice this skill in Dolphin

  1. Read the question and name the tested skill before looking at the choices.
  2. Write the equation, rule, or passage relationship in plain language.
  3. Eliminate answers that violate the setup or overstate the evidence.
  4. Review misses by writing the exact trap that pulled you toward the wrong answer.
Practice systems word problems in Dolphin SAT

Related practice

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Skill cluster

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FAQ

Questions about SAT Systems Word Problems Practice

What is the best way to practice SAT Systems Word Problems Practice?

Start with a few focused examples, review the mistake pattern, then mix the skill into full SAT practice so you can recognize it in context.

Why does this skill matter on the SAT?

It shows up in short, high-leverage questions where one missed rule or setup can quickly cost a point.

Can Dolphin SAT help me drill this skill?

Yes. Dolphin SAT can surface targeted practice, track missed questions, and help you review the patterns that keep repeating.