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SAT Math: Linear Equations (Drill 1)

Drill 1 · Math · Linear Equations

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About This Drill

SAT Math: Linear Equations (Drill 1) is a Math practice drill covering Linear Equations. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT linear equation questions ask you to solve for a variable, interpret the meaning of slope, y-intercept, or other constants in real-world context, and rewrite equations in equivalent forms. This drill includes both pure algebra and applied word problems.

Questions & Explanations

Question 1. If 3x + 7 = 28, what is the value of x?

  • A) 5
  • B) 6
  • C) 7 ✓
  • D) 9

Explanation: Subtract 7 from both sides: 3x = 21. Divide both sides by 3: x = 7.

Question 2. A plumber charges a flat fee of $75 for a house call plus $45 for each hour of labor. The total cost C, in dollars, for h hours of labor is given by C = 45h + 75. What does the number 45 represent in this equation?

  • A) The additional cost, in dollars, for each hour of labor ✓
  • B) The total cost for one hour of labor
  • C) The flat fee for a house call
  • D) The number of hours the plumber works

Explanation: In the equation C = 45h + 75, the coefficient of h is 45. This represents the rate of change, the additional cost per hour of labor. The constant 75 represents the flat fee.

Question 3. The formula F = (9/5)C + 32 converts a temperature from degrees Celsius to degrees Fahrenheit. Which of the following correctly expresses C in terms of F?

  • A) C = (5/9)F + 32
  • B) C = (9/5)(F − 32)
  • C) C = (5/9)F − 32
  • D) C = (5/9)(F − 32) ✓

Explanation: Start with F = (9/5)C + 32. Subtract 32: F − 32 = (9/5)C. Multiply by 5/9: (5/9)(F − 32) = C. The parentheses are essential; you must subtract 32 before multiplying by 5/9.

Question 4. A gym offers two membership plans. Plan A costs $30 per month with no enrollment fee. Plan B costs $18 per month plus a one-time enrollment fee of $120. After how many months will the total cost of Plan A equal the total cost of Plan B?

  • A) 8
  • B) 10 ✓
  • C) 12
  • D) 15

Explanation: Set the costs equal: 30m = 18m + 120. Subtract 18m: 12m = 120. Divide by 12: m = 10 months. After 10 months, both plans cost $300.

Question 5. If (2/3)x − 4 = 12, what is the value of x?

  • A) 12
  • B) 18
  • C) 24 ✓
  • D) 28

Explanation: Add 4 to both sides: (2/3)x = 16. Multiply both sides by 3/2: x = 16 × (3/2) = 24.