dolphin
Get Started

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 SATPractice questions
12-18 min practice time3 questions on pageAlgebra
Practice time12-18 min
Question bank3 questions
Best forAlgebra

What this tests

What to know for this SAT skill

Dolphin question bank

Practice your skill

Question 1 of 3Easy
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 solution
Correct answerA. 5s + 8a

Solution walkthrough

  1. Multiply each ticket type by its price and add the totals.
Question 2 of 3Medium
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 solution
Correct answerB. 8

Solution walkthrough

  1. Let a be adult tickets and s be student tickets. s + a = 20 and 5s + 8a = 124.
  2. Substituting s = 20 - a gives 100 + 3a = 124, so a = 8.
Question 3 of 3Hard
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 solution
Correct answerC. 22

Solution walkthrough

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

Avoid these traps

Common mistakes on this skill

Writing two equations that express the same condition

A solvable two-variable system needs two independent relationships from the problem.

Losing track of what each variable represents

An algebraically correct value can answer the wrong quantity if variables and units are not defined first.

Study plan

How to practice this skill in Dolphin

  1. Define both variables with units.
  2. Translate each distinct total, rate, price, or comparison into its own equation.
  3. Solve the system and substitute both values into both original conditions.
Practice systems word problems in Dolphin SAT

Related practice

Build the surrounding skills

SAT Math skill hubSAT Reading and Writing skill hubDolphin SAT study guidesSAT score guides by college

Skill cluster

Keep practicing SAT Math

SAT Math skill hubSAT Linear Equations PracticeSAT Systems of Equations PracticeSAT Linear Functions PracticeSAT Quadratic Equations PracticeSAT Percentages PracticeSAT Ratios and Proportions PracticeSAT Probability PracticeSAT Geometry PracticeSAT Right Triangles PracticeSAT Data Analysis PracticeSAT Circle Equations PracticeSAT Exponential Functions PracticeSAT Inequalities PracticeSAT Equivalent Expressions PracticeSAT Systems of Inequalities PracticeSAT Absolute Value Equations PracticeSAT Function Notation PracticeSAT Polynomials PracticeSAT Scatterplots PracticeSAT Mean and Median PracticeSAT Unit Conversions PracticeSAT Exponent Rules PracticeSAT Quadratic Word Problems PracticeSAT Slope-Intercept Form PracticeSAT Area and Volume PracticeSAT Percent Change PracticeSAT Trigonometry PracticeSAT Rational Equations PracticeSAT Radical Equations PracticeSAT Conditional Probability PracticeSAT Sampling and Margin of Error PracticeSAT Statistical Claims PracticeSAT Reading and Writing Practice PagesDolphin SAT study guidesSAT score guides by college

FAQ

Questions about SAT Systems Word Problems Practice

How do I know a word problem needs a system?

It usually gives two unknown quantities and two independent relationships connecting them.

Should I use substitution or elimination?

Use the method that requires less manipulation; both are valid when performed correctly.