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SAT Saturday: Linear Equations & Factoring

September 12, 2026

SAT Saturday: Linear Equations & Quadratic Expressions

Algebra study notebook displaying factored quadratic equations and linear graph notes. — Image by MyTutorLesson

Navigating the Digital SAT Math section requires both strategic word-problem setup and swift algebraic execution. From practical linear models — like calculating total weekly wages — to factoring quadratic equations without reaching for a calculator, building mastery over algebraic expressions keeps test takers efficient. Incorporating weekly practice problems into your study schedule builds test familiarity, sharpens problem-solving pacing, and helps high schoolers secure top-tier scores.

Question 39 (Linear Equations — Grid-In Style)

Marcus works at a local hardware store in Yalaha, FL, and earns a base wage of $15 per hour. He also receives a weekly flat bonus of $45 regardless of how many hours he works. If Marcus wants to earn exactly $405 this week, how many hours, does he need to work?

Question 40 (Quadratic Equations — Multiple Choice)

What is the positive value of that satisfies the equation below?

x² — 5x — 24 = 0

A. — 3
B. 8
C. 11
D. 24

💡 Week 19 Solutions & Answer Key

Question 37 (Systems of Linear Equations — Grid-In Style)

A community theater sells two types of tickets for a weekend play: adult tickets for $15 each and student tickets for $10 each. For one performance, the theater sold a total of 130 tickets and collected $1,650 in total ticket revenue. How many adult tickets did the theater sell for this performance?

Correct Answer: 70

The Concept: Set up a system of two linear equations representing total quantity and total dollar value, then solve using elimination or substitution.

Build the System: Let A be the number of adult tickets and S be the number of student tickets.
- Ticket Count Equation: A + S = 130
- Revenue Equation: 15A + 10S = 1650
Eliminate : Multiply the ticket count equation by –10: –10A – 10S = –1300
Combine & Solve: Add this equation directly to the revenue equation:

15A + 10S – 10A – 10S = 1650 – 1300

5A = 350

A = 70

Question 38 (Statistics & Mean — Multiple Choice)

Correct Answer: C (17)

The Concept: The arithmetic mean formula is Mean = (sum of terms)/(number of terms), which re-arranges to sum = mean(number of terms).

Calculate Total Sum: The sum of the original 6 numbers is 6 (12) = 72.
Calculate New Sum: The sum of the remaining 5 numbers is 5 (11) = 55.
Find Removed Value: Subtract the new sum from the original sum: 72 – 55 = 17

Build Unshakable SAT Math Confidence

Mastering SAT Math comes down to consistent practice, pattern recognition, and solid foundational math mechanics. When students learn to break down word problems into straightforward equations and execute quadratic factoring with ease, standardized testing becomes far less intimidating. Dedicated review and diagnostic feedback pave the clearest path toward achieving target SAT scores and opening doors to top college opportunities.

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