Practice Math — Algebra questions for the Scholastic Assessment Test. Every question includes a full explanation of why the correct answer is right and why the tempting distractors are wrong.
15 questions available · medium difficulty · SAT · Free, no registration required
10 example questions with full explanations. Use the interactive practice above to work through the complete set.
Question 1medium
A plumber charges a flat fee of $75 for a service visit plus $50 per hour of work. A customer's total bill was $275. Which equation represents this situation, and how many hours did the plumber work?
- A.75h + 50 = 275; h = 3 hours
- B.50h + 75 = 275; h = 4 hours✓
- C.50h + 75 = 275; h = 3 hours
- D.125h = 275; h = 2.2 hours
Correct answer: B
The flat fee of $75 is a fixed cost added to $50 multiplied by the number of hours h, giving 50h + 75 = 275. Subtracting 75 from both sides yields 50h = 200, so h = 4 hours. Choice A incorrectly swaps the roles of 75 and 50. Choice C uses the correct equation but makes an arithmetic error, getting h = 3 instead of 4. Choice D incorrectly combines the two rates into a single rate, ignoring the flat fee structure.
Question 2medium
Two friends are saving money. Marcus has $120 and saves $15 per week. Priya has $30 and saves $25 per week. After how many weeks will they have the same amount of money?
- A.7 weeks
- B.10 weeks
- C.9 weeks✓
- D.12 weeks
Correct answer: C
Setting the two savings expressions equal: 120 + 15w = 30 + 25w. Subtracting 15w from both sides gives 120 = 30 + 10w, and subtracting 30 gives 90 = 10w, so w = 9 weeks. This is a classic system-of-equations problem solved by setting two linear expressions equal.Acommon error is subtracting the starting amounts incorrectly or dividing by the wrong difference in rates, which leads to distractors like 7 or 12 weeks.
Question 3medium
The graph of a line passes through the points (2, 5) and (6, 13). What is the equation of the line?
- A.y = 3x − 1
- B.y = 2x + 3
- C.y = 4x − 3
- D.y = 2x + 1✓
Correct answer: D
First, find the slope: m = (13 − 5) / (6 − 2) = 8 / 4 = 2. Then use point-slope form with point (2, 5): y − 5 = 2(x − 2), which simplifies to y = 2x + 1. Checking: when x = 6, y = 2(6) + 1 = 13. ✓ Choice B has the correct slope but an incorrect y-intercept, a common error when students mis-substitute the point. Choices A and C use incorrect slopes derived from adding rather than dividing the differences.
Question 4medium
A scientist models the temperature T (in degrees Celsius) of a cooling liquid using the equation T = −3.5h + 98, where h is the number of hours since the experiment began. What is the best interpretation of the value −3.5 in this equation?
- A.The temperature of the liquid decreases by 3.5°C every hour.✓
- B.The liquid starts at −3.5°C at the beginning of the experiment.
- C.The experiment lasts 3.5 hours in total.
- D.The liquid reaches 0°C after 3.5 hours.
Correct answer: A
In the linear model T = −3.5h + 98, the coefficient of h is the slope, which represents the rate of change of temperature with respect to time.Bslope of −3.5 means the temperature decreases by 3.5°C for each additional hour. Choice A confuses the slope with the y-intercept; 98 is the starting temperature. Choice C misidentifies the slope as a duration. Choice D would require solving −3.5h + 98 = 0, which gives h ≈ 28 hours, not 3.5 hours.
Question 5medium
A school drama club is selling tickets to its spring play. Adult tickets cost $8 each and student tickets cost $5 each. The club needs to raise at least $400 from ticket sales. If the club sells exactly 30 student tickets, what is the minimum number of adult tickets they must sell to meet their goal?
Correct answer: B
Set up the inequality: 8a + 5(30) ≥ 400, where a is the number of adult tickets. This simplifies to 8a + 150 ≥ 400, then 8a ≥ 250, so a ≥ 31.25. Since the number of tickets must be a whole number, the minimum number of adult tickets is 32. Choice B(31) is wrong because 8(31) + 150 = 398, which is less than $400. Choices A and D reflect arithmetic errors in setting up or solving the inequality.
Question 6medium
If 3(2x − 4) + 5 = 2(x + 3) − 1, what is the value of x?
- A.x = 0
- B.x = 2
- C.x = 3✓
- D.x = 4
Correct answer: C
Expand both sides: 6x − 12 + 5 = 2x + 6 − 1, which simplifies to 6x − 7 = 2x + 5. Subtract 2x from both sides: 4x − 7 = 5. Add 7: 4x = 12, so x = 3. Choice B (x = 2) results from a distribution error on the left side. Choice D (x = 4) comes from a sign error when moving terms. Always distribute carefully and combine like terms before solving.
Question 7medium
Line ℓ passes through the points (−2, 7) and (4, −5). Line m is parallel to line ℓ and passes through the point (0, 3). At what point does line m cross the x-axis?
- A.(1, 0)
- B.(2, 0)
- C.(3, 0)
- D.(1.5, 0)✓
Correct answer: D
First, find the slope of line ℓ: m = (−5 − 7) / (4 − (−2)) = −12 / 6 = −2. Since line m is parallel to ℓ, it has the same slope of −2. Line m passes through (0, 3), so its equation is y = −2x + 3. To find the x-intercept, set y = 0: 0 = −2x + 3, so x = 1.5. Choice A (1, 0) results from a slope calculation error. Choices B and C reflect errors in setting up or solving for the x-intercept.
Question 8medium
A gym membership plan charges a one-time registration fee plus a fixed monthly fee. After 3 months, a member has paid a total of $135. After 7 months, the same member has paid a total of $255. Which equation correctly models the total cost C, in dollars, after m months?
- A.C = 30m + 45✓
- B.C = 30m + 75
- C.C = 40m + 15
- D.C = 45m + 30
Correct answer: A
The monthly fee is the rate of change: (255 − 135) / (7 − 3) = 120 / 4 = $30 per month. To find the registration fee (y-intercept), substitute one data point: 135 = 30(3) + b → 135 = 90 + b → b = 45. So the equation is C = 30m + 45. Choice B uses the correct monthly fee but places one of the data-point values as the intercept instead of solving for it. Choice C results from a division error in finding the monthly rate. Choice D swaps the monthly fee and the intercept.
Question 9medium
A store sells two types of juice: orange juice for $3 per bottle and apple juice for $2 per bottle. On Monday, the store sold a total of 50 bottles and collected $120 in revenue. How many bottles of orange juice were sold?
Correct answer: B
Set up the system: let o = orange juice bottles and a = apple juice bottles. The two equations are o + a = 50 and 3o + 2a = 120. From the first equation, a = 50 − o. Substitute: 3o + 2(50 − o) = 120 → 3o + 100 − 2o = 120 → o = 20. Choice A (15) results from a subtraction error after substitution. Choice C (25) comes from incorrectly assuming equal quantities. Choice D (30) reverses the prices of the two juice types when setting up the revenue equation.
Question 10medium
A car rental company charges a flat fee of $40 plus $0.25 per mile driven. A competing company charges a flat fee of $25 plus $0.35 per mile driven. For what number of miles driven will the total cost be the same at both companies?
Correct answer: C
Set the two cost expressions equal: 40 + 0.25m = 25 + 0.35m. Subtracting 0.25m from both sides gives 40 = 25 + 0.10m. Subtracting 25 gives 15 = 0.10m, so m = 150. At 150 miles, both companies charge $40 + $37.50 = $77.50, confirming the answer. Choice A results from a division error, and choices B and D come from incorrectly combining the flat fees or per-mile rates.