Algebraic expressions · Ages 12–13

Situations into algebra worksheet

Part of: Algebraic expressions & sequences

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Algebraic expressions · Ages 12–13

Numsprite
numsprite.com

Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A rectangle is x cm long, and its width is 8 cm less. Width = (x − ) cm; perimeter = (x − ) cm.
Fill in each blank
Answer:
2.x hours 35 minutes = (x + 35) minutes; with x = 5, that is minutes.
Fill in each blank
Answer:
3.A rectangle is x cm long, and its width is 3 cm less. Width = (x − ) cm; perimeter = (x − ) cm.
Fill in each blank
Answer:

4.May has $200 and buys x cup noodles at $27 each. How many dollars change should May get?
- A. 200 − 27 − x
- B. 200 − 27x
- C. 27x − 200
- D. (200 − 27)x
Choose the right answer
Answer:
5.One storybook costs $23. How many dollars do n storybooks cost?
- A. 23 + n
- B. 23n
- C. n − 23
- D. n23
Choose the right answer
Answer:
6.One ballpoint pen costs $10. How many dollars do n ballpoint pens cost?
- A. n10
- B. 10n
- C. 10 + n
- D. n − 10
Choose the right answer
Answer:
7.Ming has $50 and buys x erasers at $16 each. How many dollars change should Ming get?
- A. (50 − 16)x
- B. 50 − 16x
- C. 50 − 16 − x
- D. 16x − 50
Choose the right answer
Answer:
8.Tsz-hin is x years old, and Dad is 37 years older. How old will Dad be in 7 years?
- A. x + 30
- B. x + 37
- C. x + 44
- D. x + 7
Choose the right answer
Answer:
9.A car goes at v km an hour for t hours, then at 80 km an hour for 4 hours. How many km is that in all?
- A. v + t + 320
- B. vt + 84
- C. vt + 320
- D. (v + 80)(t + 4)
Choose the right answer
Answer:
10.Pens cost $18 each and notebooks $13 each. x pens and y notebooks cost 18x + 13y dollars.
True or false?
Answer:
11.Pens cost $16 each and notebooks $7 each. x pens and y notebooks cost 7x + 16y dollars.
True or false?
Answer:
12.A car goes at v km an hour for t hours, then at 50 km an hour for 4 hours. How many km is that in all?
- A. v + t + 200
- B. vt + 54
- C. (v + 50)(t + 4)
- D. vt + 200
Choose the right answer
Answer:

13.A shopkeeper has 114 shells and gives 5 to each of n customers. How many are left?
- A. 5n − 114
- B. 114 − 5 − n
- C. 114 − 5n
- D. (114 − 5)n
Choose the right answer
Working:
Answer:
14.A boy is x and his brother 5 years older. Their ages add to 2x + ; in 3 years, to 2x + .
Fill in each blank
Working:
Answer:
15.Two towns are 170 km apart. A car goes at v km an hour. How many hours does the trip take?
- A. v170
- B. 170v
- C. 170v
- D. 170 − v
Choose the right answer
Working:
Answer:
16.A cinema has 18 rows of x seats, with y people seated. Empty seats: (x − y); with x = 10 and y = 34, .
Fill in each blank
Working:
Answer:
17.A taxi charges $26 for the first 2 km, then $3 a km. How many dollars is a ride of n km (n more than 2)?
- A. 26 + 3(n − 2)
- B. 32 + 3n
- C. (26 + 3)n
- D. 26 + 3n
Choose the right answer
Working:
Answer:
18.An isosceles triangle has a base of x cm, and its two equal sides are each 15 cm longer than the base. What is its perimeter in cm?
- A. 3x + 45
- B. 2x + 15
- C. 3x + 15
- D. 3x + 30
Choose the right answer
Working:
Answer:

Show the answers and working

Situations into algebra worksheet: Answers and working

1. 8, 4, 16
Perimeter = x + x + (x − 8) + (x − 8) = 4x − 16.
2. 60, 335
One hour has 60 minutes, so x hours have 60x. Put in the number: 60 × 5 + 35 = 335.
3. 3, 4, 6
Perimeter = x + x + (x − 3) + (x − 3) = 4x − 6.

4. B. 200 − 27x
The total is 27x dollars, so the change is 200 − 27x dollars.
5. B. 23n
Three cost 23 × 3 dollars, so n cost 23 × n = 23n dollars.
6. B. 10n
Three cost 10 × 3 dollars, so n cost 10 × n = 10n dollars.
7. B. 50 − 16x
The total is 16x dollars, so the change is 50 − 16x dollars.
8. C. x + 44
Dad is x + 37 now, and in 7 years x + 37 + 7 = x + 44.
9. C. vt + 320
Distance = speed × time: vt for the first part, 80 × 4 = 320 for the second: vt + 320.
10. True
x pens cost 18x dollars and y notebooks 13y, so 18x + 13y in all.
11. False
x pens cost 16x dollars and y notebooks 7y, so 16x + 7y in all.
12. D. vt + 200
Distance = speed × time: vt for the first part, 50 × 4 = 200 for the second: vt + 200.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. C. 114 − 5n
5n go out, so 114 − 5n are left.
14. 5, 11
x + (x + 5) = 2x + 5. In 3 years each is 3 older, so the sum grows by 6: 2x + 11.
15. B. 170v
Time = distance ÷ speed = 170 ÷ v = 170v. With a real number: at 10 km an hour, it takes 170 ÷ 10 hours.
16. 18, 146
18x seats in all, less y: 18 × 10 − 34 = 180 − 34 = 146.
17. A. 26 + 3(n − 2)
$26 for the first 2 km, and n − 2 km more at $3: 26 + 3(n − 2).
18. D. 3x + 30
x + (x + 15) + (x + 15) = 3x + 30.

Numsprite · numsprite.com/en/worksheets/algebraic-expressions-and-sequences/writing-expressions-from-situations