Math Writing Questions — Questions and Answers
Question 1: A word problem states: 'Sarah earns $15 per hour and works h hours. She also receives a $50 bonus.' Which equation represents her total earnings T?
- T = 15h + 50 (Correct answer)
- T = 50h + 15
- T = 15 + 50h
- T = 15h - 50
Correct answer: T = 15h + 50
Total earnings equals the hourly rate times hours worked plus the flat bonus: T = 15h + 50.
Question 2: Which inequality represents 'a number x is at most 12'?
- x ≤ 12 (Correct answer)
- x < 12
- x ≥ 12
- x > 12
Correct answer: x ≤ 12
'At most 12' means x can equal 12 or be less, so x ≤ 12.
Question 3: A tank holds 200 gallons and drains at 4 gallons per minute. Which expression gives the amount W remaining after m minutes?
- W = 200 - 4m (Correct answer)
- W = 4m - 200
- W = 200 + 4m
- W = 200 ÷ 4m
Correct answer: W = 200 - 4m
Starting volume minus the drain rate times minutes gives W = 200 - 4m.
Question 4: Which expression represents 'three less than twice a number n'?
- 2n - 3 (Correct answer)
- 3 - 2n
- 2(n - 3)
- 3n - 2
Correct answer: 2n - 3
'Twice a number' is 2n, and 'three less than' means subtract 3, giving 2n - 3.
Question 5: A store marks up items by 20%. If an item costs the store $c, which expression gives the selling price S?
- S = 1.2c (Correct answer)
- S = c + 20
- S = 0.2c
- S = c - 0.2c
Correct answer: S = 1.2c
A 20% markup means multiplying the cost by 1.20, so S = 1.2c.
Question 6: Which equation models 'the sum of two consecutive integers equals 47'?
- n + (n + 1) = 47 (Correct answer)
- n + (n + 2) = 47
- 2n = 47
- n(n + 1) = 47
Correct answer: n + (n + 1) = 47
Consecutive integers differ by 1, so the two numbers are n and n+1, and their sum is 47.
Question 7: A recipe requires r cups of flour for 12 cookies. Which expression gives the cups needed for 60 cookies?
- 5r (Correct answer)
- r + 60
- 60r
- r/5
Correct answer: 5r
60 cookies is 5 times 12 cookies, so you need 5r cups of flour.
Question 8: A gym charges a $30 enrollment fee plus $25 per month. Which equation gives the total cost C after m months?
- C = 25m + 30 (Correct answer)
- C = 30m + 25
- C = 25 + 30m
- C = 55m
Correct answer: C = 25m + 30
The one-time fee is 30 and the recurring monthly charge is 25m, giving C = 25m + 30.
Question 9: Which expression represents 'the quotient of a number n and 4, increased by 7'?
- n/4 + 7 (Correct answer)
- n/(4 + 7)
- 4/n + 7
- (n + 7)/4
Correct answer: n/4 + 7
'Quotient of n and 4' is n÷4, and 'increased by 7' adds 7, giving n/4 + 7.
Question 10: A population of 500 bacteria doubles every hour. Which expression gives the population P after h hours?
- P = 500 · 2^h (Correct answer)
- P = 500 + 2h
- P = 2 · 500h
- P = 500h^2
Correct answer: P = 500 · 2^h
Doubling each hour is exponential growth: P = 500 · 2^h.
Question 11: Which inequality represents 'a number y is more than 5 units away from zero'?
- |y| > 5 (Correct answer)
- |y| < 5
- y > 5
- y < -5
Correct answer: |y| > 5
Distance from zero is absolute value, and 'more than 5' means |y| > 5.
Question 12: A car travels at a constant speed of s mph. Which expression gives the distance d after t hours if it started 10 miles ahead?
- d = st + 10 (Correct answer)
- d = s + 10t
- d = 10st
- d = st - 10
Correct answer: d = st + 10
Distance equals speed × time, plus the head-start of 10 miles: d = st + 10.
Question 13: Which equation represents 'five times the difference of a number x and 3 equals 20'?
- 5(x - 3) = 20 (Correct answer)
- 5x - 3 = 20
- 5x + 3 = 20
- (5 - 3)x = 20
Correct answer: 5(x - 3) = 20
'Difference of x and 3' is (x - 3), and multiplying by 5 gives 5(x - 3) = 20.
Question 14: A triangle has a perimeter of 36 cm. Two sides measure x and 2x. Which equation finds x?
- x + 2x + (36 - 3x) = 36
- 4x = 36 (Correct answer)
- 3x + third side = 36
- x + 2x = 36
Correct answer: 4x = 36
If the three sides are x, 2x, and the remaining side, we need more info; but if the third side equals x, then x + 2x + x = 4x = 36.
Question 15: A runner completes a race in t minutes. A second runner finishes 8 minutes faster. Which expression gives the second runner's time?
- t - 8 (Correct answer)
- t + 8
- 8t
- t/8
Correct answer: t - 8
'Faster' means less time, so the second runner's time is t - 8.
Question 16: Which equation represents 'half of a number increased by 9 is 21'?
- n/2 + 9 = 21 (Correct answer)
- n/2 - 9 = 21
- (n + 9)/2 = 21
- 2n + 9 = 21
Correct answer: n/2 + 9 = 21
'Half of n' is n/2, and 'increased by 9' gives n/2 + 9 = 21.
Question 17: A vendor sells apples for $0.50 each and oranges for $0.75 each. Which expression gives the total cost for a apples and g oranges?
- 0.50a + 0.75g (Correct answer)
- 0.75a + 0.50g
- (0.50 + 0.75)(a + g)
- 1.25(a + g)
Correct answer: 0.50a + 0.75g
Multiply each item's price by its quantity and add: 0.50a + 0.75g.
Question 18: Which inequality represents 'the product of 3 and a number x is no less than 15'?
- 3x ≥ 15 (Correct answer)
- 3x ≤ 15
- 3x > 15
- 3x < 15
Correct answer: 3x ≥ 15
'No less than' means 'greater than or equal to,' so 3x ≥ 15.
Question 19: A pool is being filled at 8 gallons per minute and simultaneously drained at 3 gallons per minute. Which expression gives the net gallons after m minutes?
- 5m (Correct answer)
- 11m
- 8m
- 3m
Correct answer: 5m
Net fill rate is 8 - 3 = 5 gallons per minute, so the net gallons after m minutes is 5m.
Question 20: Which expression represents 'the square of the sum of x and 4'?
- (x + 4)² (Correct answer)
- x² + 4
- x² + 16
- x + 4²
Correct answer: (x + 4)²
'The sum of x and 4' is (x + 4), and squaring it gives (x + 4)².
Question 21: A phone plan costs $40 per month plus $0.10 per text message. If a user sends t texts and has a $55 budget, which inequality must hold?
- 40 + 0.10t ≤ 55 (Correct answer)
- 40 + 0.10t ≥ 55
- 0.10t ≤ 55
- 40t + 0.10 ≤ 55
Correct answer: 40 + 0.10t ≤ 55
Total cost 40 + 0.10t must not exceed the $55 budget, so 40 + 0.10t ≤ 55.
