GED Algebra Practice Questions, Set 3

This is set 3 of 4 for GED Algebra, with 22 practice questions that are not part of any full practice test. If a question type feels unfamiliar, review the Algebra study guide first, then check each answer below.

Question 1 of 22

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A water bill is modeled by B = 0.006g + 18, where g is gallons used. A household used 4,500 gallons in June and 7,000 gallons in July. How much more was the July bill than the June bill?

Algebra practice set 3: 22 questions with answers

Work each question on paper first, then open the answer to check your reasoning.

  1. 1.A water bill is modeled by B = 0.006g + 18, where g is gallons used. A household used 4,500 gallons in June and 7,000 gallons in July. How much more was the July bill than the June bill?

    1. A.$60
    2. B.$45
    3. C.$15
    4. D.$33
    Show answer

    Answer: C. $15

    Only the usage term changes: 0.006 × (7,000 − 4,500) = 0.006 × 2,500 = $15. Choice $60 is the full July bill, 42 + 18, not the difference.

  1. 2.The table shows the fuel left in a generator. Hours running: 0, 2, 4, 6 Fuel (gallons): 60, 52, 44, 36 If the pattern continues, after how many hours will the tank be empty?

    1. A.15 hours
    2. B.9 hours
    3. C.7.5 hours
    4. D.12 hours
    Show answer

    Answer: A. 15 hours

    Fuel drops 8 gallons every 2 hours, which is 4 gallons per hour. Starting from 60 gallons, 60 ÷ 4 = 15 hours. Choice 7.5 hours treats the drop of 8 gallons as if it happened every hour.

  1. 3.Solve for x: 9 − (x − 4) = 3x + 1

    1. A.x = 4
    2. B.x = 3
    3. C.x = 1
    4. D.x = −3
    Show answer

    Answer: B. x = 3

    Distribute the negative: 9 − x + 4 = 3x + 1, so 13 − x = 3x + 1 and 12 = 4x, giving x = 3. Choice x = 1 comes from writing −(x − 4) as −x − 4.

  1. 4.The perimeter of a rectangle is P = 2L + 2W. Which equation is solved for W?

    1. A.W = (P − 2L)/2
    2. B.W = 2(P − 2L)
    3. C.W = (P + 2L)/2
    4. D.W = P/2 − 2L
    Show answer

    Answer: A. W = (P − 2L)/2

    Subtract 2L from both sides to get P − 2L = 2W, then divide by 2. Choice W = P/2 − 2L divides only P by 2 and leaves 2L unchanged.

  1. 5.A hotel shuttle carries 4 more than twice as many passengers as a car. Together, the shuttle and the car carry 19 passengers. How many passengers does the shuttle carry?

    1. A.14
    2. B.10
    3. C.15
    4. D.5
    Show answer

    Answer: A. 14

    Let c be the car’s passengers: c + (2c + 4) = 19, so 3c = 15 and c = 5. The shuttle carries 2(5) + 4 = 14. Choice 5 is the number in the car.

  1. 6.An internet plan costs $15 more per month than a phone plan. A family pays $1,140 a year for both plans together. What is the monthly cost of the phone plan?

    1. A.$47.50
    2. B.$40
    3. C.$55
    4. D.$80
    Show answer

    Answer: B. $40

    Both plans cost $1,140 ÷ 12 = $95 a month, so p + (p + 15) = 95 gives 2p = 80 and p = $40. Choice $55 is the monthly cost of the internet plan.

  1. 7.Which number line graph shows the solution of 2x + 5 > 11?

    1. A.Open dot at 3, shaded to the left
    2. B.Open dot at 8, shaded to the right
    3. C.Closed dot at 3, shaded to the right
    4. D.Open dot at 3, shaded to the right
    Show answer

    Answer: D. Open dot at 3, shaded to the right

    Subtract 5 and divide by 2 to get x > 3. A strict inequality uses an open dot, and greater than shades to the right. A closed dot would include 3, which does not make the inequality true.

  1. 8.A line has the equation 3x + 5y = 15. What are its slope and y-intercept?

    1. A.slope 3/5, y-intercept 3
    2. B.slope −3, y-intercept 15
    3. C.slope −3/5, y-intercept 3
    4. D.slope −5/3, y-intercept 5
    Show answer

    Answer: C. slope −3/5, y-intercept 3

    Solve for y: 5y = −3x + 15, so y = −(3/5)x + 3. Choice slope 3/5 drops the negative sign when 3x moves to the other side.

  1. 9.The table shows a function. x: 0, 1, 2, 3 y: 2, 5, 10, 17 Which equation fits every pair in the table?

    1. A.y = x² + 2x + 2
    2. B.y = 2x² + x + 2
    3. C.y = 3x + 2
    4. D.y = x² + 3x − 1
    Show answer

    Answer: A. y = x² + 2x + 2

    Check each pair in y = x² + 2x + 2: 0 + 0 + 2 = 2, 1 + 2 + 2 = 5, 4 + 4 + 2 = 10, and 9 + 6 + 2 = 17. Choice y = 3x + 2 fits the first two pairs but gives 8 when x = 2.

  1. 10.Which ordered pair is the solution of the system 4x + y = 9 and x − y = 6?

    1. A.(3, −3)
    2. B.(2, 1)
    3. C.(3, 3)
    4. D.(−3, 3)
    Show answer

    Answer: A. (3, −3)

    Add the equations to get 5x = 15, so x = 3, and then 3 − y = 6 gives y = −3. Choice (3, 3) works in neither equation: 4(3) + 3 = 15, not 9.

  1. 11.Factor completely: 5x² − 45

    1. A.(5x − 9)(x + 5)
    2. B.5(x − 3)(x + 3)
    3. C.(x − 5)(5x + 9)
    4. D.5(x − 9)(x + 1)
    Show answer

    Answer: B. 5(x − 3)(x + 3)

    Factor out 5 to get 5(x² − 9), then factor the difference of squares: 5(x − 3)(x + 3). Choice 5(x − 9)(x + 1) expands to 5x² − 40x − 45, which has an extra x term.

  1. 12.For what values of x does x² − 8x + 12 = 0?

    1. A.x = −2 or x = −6
    2. B.x = 1 or x = 12
    3. C.x = 3 or x = 4
    4. D.x = 2 or x = 6
    Show answer

    Answer: D. x = 2 or x = 6

    Factor as (x − 2)(x − 6) = 0, so x = 2 or x = 6. Choice x = −2 or x = −6 uses the wrong signs: those values solve x² + 8x + 12 = 0.

  1. 13.Simplify: (15a⁵b²) / (5a²b⁻¹)

    1. A.3a⁷b
    2. B.10a³b³
    3. C.3a³b
    4. D.3a³b³
    Show answer

    Answer: D. 3a³b³

    Divide 15 by 5 to get 3, subtract exponents for a (5 − 2 = 3), and for b (2 − (−1) = 3). Choice 3a³b subtracts 1 from the b exponent instead of subtracting −1.

  1. 14.Which expression is equivalent to (x + 3)² − x²?

    1. A.6x + 3
    2. B.9
    3. C.3x + 9
    4. D.6x + 9
    Show answer

    Answer: D. 6x + 9

    (x + 3)² = x² + 6x + 9, and subtracting x² leaves 6x + 9. Choice 9 comes from squaring as x² + 9, which leaves out the middle term 6x.

  1. 15.A taxi fare in dollars is modeled by F = 2.75m + 3.50, where m is the number of miles. What does 2.75 represent?

    1. A.The fare for a 1-mile ride
    2. B.The fixed charge at pickup
    3. C.The charge for each mile
    4. D.The number of miles in a ride
    Show answer

    Answer: C. The charge for each mile

    In a linear model, the number multiplied by the variable is the rate, so the fare rises $2.75 for each mile. The fixed charge at pickup is the $3.50 that does not depend on miles.

  1. 16.The table shows a savings account balance. Week: 0, 3, 6, 9 Balance ($): 260, 404, 548, 692 If the pattern continues, in which week will the balance first reach at least $1,000?

    1. A.Week 15
    2. B.Week 21
    3. C.Week 16
    4. D.Week 18
    Show answer

    Answer: C. Week 16

    The balance rises $144 every 3 weeks, or $48 a week, so 260 + 48w ≥ 1,000 gives w ≥ 15.4. Week 15 has only $980, so the first week is Week 16. Choice Week 15 rounds 15.4 down.

  1. 17.A 90-inch ribbon is cut into two pieces. The longer piece is 4 times as long as the shorter piece. How long is the longer piece?

    1. A.22.5 inches
    2. B.18 inches
    3. C.86 inches
    4. D.72 inches
    Show answer

    Answer: D. 72 inches

    Let s be the shorter piece, so s + 4s = 90 and s = 18. The longer piece is 4 × 18 = 72 inches. Choice 18 inches is the shorter piece.

  1. 18.A salesperson earns $520 a week plus a 6% commission on sales. Last week the total pay was $856. What were the salesperson’s sales for the week?

    1. A.$14,267
    2. B.$8,667
    3. C.$5,600
    4. D.$2,016
    Show answer

    Answer: C. $5,600

    The commission was 856 − 520 = $336, and 0.06s = 336 gives s = $5,600. Choice $14,267 divides the whole $856 by 0.06, which wrongly counts the base pay as commission.

  1. 19.Which ordered pair is the solution of the system y = 3x − 4 and y = −x + 8?

    1. A.(4, 4)
    2. B.(5, 3)
    3. C.(2, 2)
    4. D.(3, 5)
    Show answer

    Answer: D. (3, 5)

    Set 3x − 4 = −x + 8, so 4x = 12 and x = 3. Then y = 3(3) − 4 = 5. The pair (2, 2) fits the first equation but not the second.

  1. 20.Gym A charges $40 to join and $25 a month. Gym B charges $100 to join and $19 a month. After how many months will the total cost at the two gyms be the same?

    1. A.12 months
    2. B.6 months
    3. C.10 months
    4. D.4 months
    Show answer

    Answer: C. 10 months

    Set 40 + 25m = 100 + 19m. Then 6m = 60, so m = 10. Choice 6 months is the difference in the monthly rates, not the number of months.

  1. 21.Which inequality describes every number x that is at most 3 units away from 5 on a number line?

    1. A.x ≤ 2 or x ≥ 8
    2. B.2 ≤ x ≤ 8
    3. C.3 ≤ x ≤ 5
    4. D.−3 ≤ x ≤ 5
    Show answer

    Answer: B. 2 ≤ x ≤ 8

    Going 3 units left of 5 reaches 2 and going 3 units right reaches 8, so x is between 2 and 8, inclusive. The choice x ≤ 2 or x ≥ 8 describes numbers at least 3 units away.

  1. 22.Solve the inequality: x/2 + 3 > 7

    1. A.x > 20
    2. B.x > 8
    3. C.x > 2
    4. D.x < 8
    Show answer

    Answer: B. x > 8

    Subtract 3 to get x/2 > 4, then multiply by 2 to get x > 8. Choice x > 2 divides by 2 instead of multiplying.

More practice sets

Algebra has 4 practice sets. None of these questions appear in the full practice tests.