WorksheetsReal-World Algebraic Expressions Challenge
Total questions: 80
Worksheet time: 40mins
Name
Class
Date
1.
1. An elevator starts at floor x. It goes up 5 floors, then goes down to a floor exactly half that height.
a)
(x + 5) / 2
b)
x + 5 / 2
c)
x / 2 + 5
d)
5x / 2
2.
2. A rectangle has a width of w. The length is 3 inches longer than twice the width. What is the length?
a)
2w - 3
b)
3w + 2
c)
2w + 3
d)
w + 3
3.
3. You have a rope of length L. You cut off 10 meters, and then divide the remaining rope into 4 equal jump ropes.
a)
(L / 4) - 10
b)
(L - 10) / 4
c)
L - 10 / 4
d)
4L - 10
4.
4. The temperature was t degrees. It dropped 4 degrees per hour for 3 hours.
a)
t - 4
b)
t - 7
c)
t - 12
d)
3t - 4
5.
5. A baker has e eggs. He uses 12 eggs for a cake, then throws away 2 cracked ones. How many are left?
a)
e - 12
b)
e - 10
c)
e - 14
d)
e - 24
6.
6. A car travels at 50 mph for h hours, then stops for 1 hour, then travels 20 more miles. Total distance?
a)
50h + 20
b)
50(h + 1) + 20
c)
50h + 70
d)
20h + 50
7.
7. There are s students. The teacher puts them into groups of 5, but there are 2 students left over. Which expression represents the number of groups?
a)
(s + 2) / 5
b)
(s - 2) / 5
c)
5s + 2
d)
s / 5 - 2
8.
8. A tree is f feet tall. It grows 2 feet per year for y years. What is the new height?
a)
f + y
b)
f + 2y
c)
2fy
d)
f + 2 + y
9.
9. A gamer scores p points in Level 1. In Level 2, they score double Level 1, plus a bonus of 50 points. Total points for Level 2 only?
a)
2p + 50
b)
p + 50
c)
2(p + 50)
d)
p^2 + 50
10.
10. A tank holds g gallons. You use half the water, then add 5 gallons back.
a)
g/2 - 5
b)
g - 5
c)
g/2 + 5
d)
2g + 5
11.
11. Sam is x years old. His brother is 4 years younger than him. His sister is 3 times the brother's age.
a)
3x - 4
b)
3(x - 4)
c)
3x - 12
d)
x - 4
12.
12. A runner runs m miles on Monday. On Tuesday, she runs 2 miles less than double Monday's distance.
a)
2m - 2
b)
2(m - 2)
c)
m/2 - 2
d)
2m + 2
13.
13. You have b boxes. Each box has 10 books. You donate 5 books from the total collection.
a)
10b - 5
b)
10(b - 5)
c)
b/10 - 5
d)
5b - 10
14.
14. A square has a side length of s. You increase the side by 3. What is the new perimeter?
a)
4s + 3
b)
4(s + 3)
c)
s + 3
d)
s^2 + 3
15.
15. A video downloads at x MB/sec. How much downloads in 2 minutes (120 seconds) plus an extra 10 MB buffer?
a)
2x + 10
b)
120x + 10
c)
x/120 + 10
d)
120(x + 10)
16.
16. A pile of sand weighs w lbs. You remove 10 lbs, then split the rest into 2 equal bags. Weight of one bag?
a)
(w/2) - 10
b)
(w - 10) / 2
c)
w - 5
d)
2w - 10
17.
17. There are z zebras. The number of lions is half the number of zebras plus 3.
a)
z/2 + 3
b)
2z + 3
c)
(z + 3) / 2
d)
z + 3/2
18.
18. A phone battery is at p percent. It drains 15% during the day, then you charge it up by 30%.
a)
p - 15 + 30
b)
p(0.85)(1.30)
c)
p - 15% + 30%
d)
p + 15
19.
19. A classroom has r rows with 6 desks each. The janitor adds 2 more rows of 6 desks.
a)
6r + 2
b)
6(r + 2)
c)
6r + 12
d)
r + 12
20.
20. You have c cookies. You eat 3. You give half of the remaining cookies to a friend.
a)
c/2 - 3
b)
(c - 3) / 2
c)
c - 3 / 2
d)
2c - 3
21.
21. A car travels x hours at 60 mph and y hours at 40 mph. What is the average speed for the whole trip?
a)
(60x + 40y) / 2
b)
(60x + 40y) / (x + y)
c)
100(x + y)
d)
50
22.
22. The width of a pool is w. The length is 2w + 5. You walk around the perimeter twice.
a)
6w + 10
b)
2(6w + 10)
c)
4(3w + 5)
d)
3w + 5
23.
23. A tank contains 100 liters. Tap A pours in x liters/min. Tap B drains y liters/min. Amount after 10 mins?
a)
100 + 10(x - y)
b)
100 + 10x - y
c)
100 + x - y
d)
10(100 + x - y)
24.
24. A test has 50 questions. You get c correct (worth 2 points) and w wrong (lose 1 point). Unanswered are 0.
a)
2c - w
b)
2c + w
c)
50 - c - w
d)
2(c - w)
25.
25. A bacteria colony starts with B. It triples every hour. After 2 hours, 500 bacteria die.
a)
3B - 500
b)
B^3 - 500
c)
9B - 500
d)
6B - 500
26.
26. You have a string of length S. You form a triangle with sides a, b, and c. How much string is left?
a)
S - (a + b + c)
b)
S - abc
c)
S / (a + b + c)
d)
a + b + c - S
27.
27. A student reads p pages on Monday. Tuesday she reads 10 more than Monday. Wednesday she reads double Tuesday's amount.
a)
4p + 30
b)
p + (p+10) + 2(p+10)
c)
3p + 20
d)
2p + 20
28.
28. An athlete runs at speed v. He increases speed by 20% for t minutes. Distance covered?
a)
1.2vt
b)
0.2vt
c)
v + 0.2t
d)
vt + 20
29.
29. A box has length L, width W, height H. You double the length and halve the height. The new volume is:
a)
LWH
b)
2LWH
c)
LWH / 2
d)
4LWH
30.
30. A project requires T total hours. Three people work on it. Person A works x hours, Person B works y hours. How many hours must Person C work?
a)
T - x - y
b)
T - (x + y)
c)
T / 3
d)
x + y - T
31.
31. Temperature is C in Celsius. To get Fahrenheit: Multiply by 1.8, then add 32. If C increases by 10, how much does F increase?
a)
10
b)
18
c)
32
d)
42
32.
32. A jar has r red marbles and b blue marbles. You add 5 red and remove 3 blue. What fraction of the marbles are now red?
a)
(r + 5) / (r + b + 2)
b)
(r + 5) / (r + b)
c)
r / (r + b)
d)
(r + 5) / (b - 3)
33.
33. A gym membership is a flat fee of F plus m per month. You join for a year (12 months) but get a discount of d on the total.
a)
F + 12m - d
b)
(F + 12m) - d
c)
F + 12(m - d)
d)
12(F + m) - d
34.
34. You have 100 liters of water. You use 10% of it, then add x liters, then use 10% of the NEW amount.
a)
0.9(90 + x)
b)
90 + 0.9x
c)
0.9(100 + x)
d)
81 + x
35.
35. The sum of three consecutive even integers is S. If the first is n, which equation describes S?
a)
3n + 3
b)
3n + 6
c)
n + n+2 + n+4
d)
n^3
36.
36. A car drives D miles. The first 100 miles are at 50 mph. The rest are at 60 mph. Total time?
a)
2 + (D - 100)/60
b)
100/50 + D/60
c)
D/110
d)
2 + D/60
37.
37. A rectangle has perimeter P. The length is L. What is the area?
a)
L(P - L)
b)
L(P - 2L)
c)
L(P/2 - L)
d)
P - 2L
38.
38. A smartphone has storage S. The OS takes 10GB. Photos take p GB. Apps take twice as much as photos. Free space?
a)
S - 10 - 3p
b)
S - 10 - 2p
c)
S - 3p
d)
S - 10 - p
39.
39. Two trains move toward each other. Train A is at speed a, Train B at speed b. They are M miles apart. Time until impact?
a)
M / (a - b)
b)
M(a + b)
c)
M / (a + b)
d)
M / ab
40.
40. A box contains x items. You take out 1/3 of them. Then you put back 4 items. How many are in the box?
a)
x/3 + 4
b)
2x/3 + 4
c)
x - 4
d)
4x/3
41.
41. Logic Gate: Input A is x. Input B is y. The output is the sum squared, minus the product.
a)
(x + y)^2 - xy
b)
x^2 + y^2 - xy
c)
(x - y)^2 + xy
d)
x^2 + y^2
42.
42. A field is L meters long and W meters wide. A path of width p is built around the OUTSIDE. Total Area including path?
a)
(L + 2p)(W + 2p)
b)
(L + p)(W + p)
c)
LW + 2p
d)
LW + 4p^2
43.
43. Water flows into a tank at rate r1 and leaks out at rate r2. If r1 > r2, how long to fill a volume V?
a)
V / (r1 + r2)
b)
V(r1 - r2)
c)
V / (r1 - r2)
d)
V / r1 - V / r2
44.
44. You have 5 piles of rocks. The first has n rocks. Each subsequent pile has 2 more rocks than the previous one. Total rocks?
a)
5n + 10
b)
5n + 20
c)
n + 10
d)
5n + 8
45.
45. A video game health bar is H. You take d damage, then heal for 50% of the REMAINING health.
a)
1.5(H - d)
b)
(H - d) + 0.5H
c)
0.5(H - d)
d)
H - d + 50
46.
46. Average of 4 numbers is A. If you remove one number k, what is the new sum of the remaining 3?
a)
4A - k
b)
A - k
c)
(4A - k) / 3
d)
3A
47.
47. A ladder is L feet long. It leans against a wall. The base is b feet from the wall. Height reaches?
a)
L - b
b)
sqrt(L - b)
c)
sqrt(L^2 - b^2)
d)
L^2 - b^2
48.
48. A fast food order: b burgers and f fries. Calories: Burger Cb, Fries Cf. You eat half the burgers and all the fries.
a)
0.5b(Cb) + f(Cf)
b)
b(Cb) + f(Cf)
c)
0.5(b + f)
d)
Cb + Cf
49.
49. Ratio of Cats to Dogs is 3:4. Total animals is T. How many dogs?
a)
3T / 7
b)
4T / 7
c)
4T / 3
d)
T / 4
50.
50. An engine runs for x hours at R rpm, then for 2 hours at half that speed. Total revolutions?
a)
60R(x + 1)
b)
60(Rx + R)
c)
Rx + R
d)
60Rx + 120(R/2)
51.
51. A car travels distance D. It travels 1/3 of the distance at speed v1 and the rest at speed v2. Total time?
a)
D/(3v1) + 2D/(3v2)
b)
D/3v1 + D/v2
c)
D/(v1 + v2)
d)
3v1 + 3v2
52.
52. A tank has salt water with concentration C (amount/vol). You evaporate 20% of the water volume V. New concentration?
a)
C
b)
0.8C
c)
1.2C
d)
1.25C
53.
53. Work rate: Machine A takes x hours to finish a job. Machine B takes y hours. If they work together for t hours, what fraction of the job is done?
a)
t(x + y)
b)
t / (x + y)
c)
t(1/x + 1/y)
d)
xy / t
54.
54. A square has area A. You double the side length. Then you cut out a circle of radius r. Remaining area?
a)
2A - pi*r^2
b)
4A - pi*r^2
c)
A^2 - pi*r^2
d)
4A - 2pi*r
55.
55. Fluid Mixing: m1 liters at Temp T1 mixed with m2 liters at Temp T2. Final Temp? (Weighted Average)
a)
(T1 + T2) / 2
b)
(m1T1 + m2T2) / (m1 + m2)
c)
m1T1 + m2T2
d)
(m1 + m2) / (T1 + T2)
56.
56. A population P grows by r percent per year. Population after 3 years?
a)
P(1 + r)^3
b)
P(1 + r/100)^3
c)
P + 3r
d)
3P(1+r)
57.
57. You have a box with dimensions x, x+2, x-2. Surface area?
a)
x^3 - 4x
b)
6x^2 - 8
c)
2(x^2 - 4) + 4x^2
d)
4x^2 + 8
58.
58. Relativity (Sort of): A clock runs s seconds slow every day. How many days until it is exactly 1 hour (3600 seconds) behind?
a)
s / 3600
b)
3600 / s
c)
3600s
d)
3600 - s
59.
59. A runner is at position x1. A second runner is at x2. At what time t do they meet if speeds are v1 and v2?
a)
(x2 - x1) / (v1 - v2)
b)
(x2 + x1) / (v1 + v2)
c)
x1v1 = x2v2
d)
v1 - v2
60.
60. Fuel Efficiency: Car A gets a mpg. Car B gets b mpg. Gallons saved by Car B over a 1000 mile trip vs Car A?
a)
1000/a - 1000/b
b)
1000(b - a)
c)
1000/b - 1000/a
d)
1000(a - b)
61.
61. A rectangle's length is increased by 10% and width decreased by 10%. New Area?
a)
A
b)
0.99A
c)
1.01A
d)
0.9A
62.
62. Variable z varies directly with x and inversely with y. Constant is k. Equation?
a)
z = kxy
b)
z = kx/y
c)
z = ky/x
d)
z = k/xy
63.
63. A test score average of 5 students is 80. A 6th student joins and the average becomes x. What did the 6th student score?
a)
6x - 400
b)
5x - 400
c)
x - 80
d)
6x - 80
64.
64. Construction: You need to cover a wall of Area A. Paint covers p sq ft per gallon. You buy g gallons. How much of the wall is UNPAINTED?
a)
A - gp
b)
gp - A
c)
A / gp
d)
g / p
65.
65. Two gears: Gear A has Na teeth, Gear B has Nb. If A turns Ta times, how many times does B turn?
a)
(Na * Ta) / Nb
b)
(Nb * Ta) / Na
c)
Na * Nb * Ta
d)
Ta / Nb
66.
66. A cube of side s is painted blue. It is cut into n^3 smaller cubes (where n is cuts per side). Total surface area of all small cubes?
a)
6s^2
b)
6n * s^2
c)
n^3 * s^2
d)
6s^2 / n
67.
67. Digit Problem: A two-digit number has tens digit t and ones digit u. You reverse the digits. The difference between the new and old number is:
a)
9(u - t)
b)
10u + t
c)
u - t
d)
9(t - u)
68.
68. Trajectory: A ball is thrown up. Height h = -16t^2 + 64t. What is the height at t = 3?
a)
16
b)
48
c)
32
d)
64
69.
69. Density: Object A has density d and volume V. Object B has density 0.5d and volume 2V. Mass ratio (Mass A / Mass B)?
a)
1
b)
2
c)
0.5
d)
4
70.
70. Shadows: A pole of height h casts a shadow s. A person of height p casts a shadow x at the same time. Relationship?
a)
h/s = x/p
b)
h/p = s/x
c)
hx = ps
d)
Both B and C
71.
71. Data Plan: You have limit L. You use x GB/day for 10 days, then y GB/day for the remaining 20 days. Data remaining?
a)
L - 10x - 20y
b)
L - (10x + 20y)
c)
L - 30(x+y)
d)
Both A and B
72.
72. Cylindrical Pipe: Inner radius r, outer radius R, length L. Volume of the material?
a)
pi*L(R - r)^2
b)
pi*L(R^2 - r^2)
c)
pi*L(R^2 + r^2)
d)
2pi*L(R - r)
73.
73. Harmonic Motion: A spring stretches x inches with weight W. If stiffness is k, then W=kx. If you double the weight, what is the new stretch?
a)
x
b)
2x
c)
x/2
d)
x^2
74.
74. In a race, A beats B by x meters. B beats C by y meters. (All run constant speed). In a race between A and C, by how much does A beat C? (Assume race length L)
a)
x + y
b)
x + y - xy/L
c)
L(x+y)
d)
x - y
75.
75. A stream speed is c. Boat speed is b. Trip upstream takes t. Distance?
a)
t(b + c)
b)
t(b - c)
c)
b/t
d)
c/t
76.
76. A photo is w inches wide. You enlarge it by scale factor k. Then you put a 2-inch border around it. Final width?
a)
kw + 2
b)
k(w + 2)
c)
kw + 4
d)
w + 2k
77.
77. Chemicals: Sol A is 10% acid. Sol B is 50% acid. You mix x liters of A and y liters of B. Total acid amount?
a)
0.1x + 0.5y
b)
0.6(x + y)
c)
10x + 50y
d)
(x+y)/2
78.
78. You plant T trees. 10% die. The rest grow 2 feet a year (y). Total growth of living trees after y years?
a)
0.9T * 2y
b)
T * 2y
c)
0.1T * 2y
d)
1.8Ty
79.
79. A widget involves 3 parts A, 2 parts B, and 1 part C. Weight of A is w. B is twice as heavy as A. C is half as heavy as A. Total weight?
a)
3w + 4w + 0.5w
b)
7.5w
c)
6w
d)
Both A and B
80.
80. Age Riddle: A is 3 times as old as B was 2 years ago. Current age of A? (Let B = current age of B)
a)
3B - 2
b)
3(B - 2)
c)
3B - 6
d)
Both B and C
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