Algebra Applications Worksheet
The Study Zone
Section 1: Age-Based Questions
1. Sarah is 5 years older than her sister, Emma. The sum of their ages is 29. How old is each sister?
2. Five years ago, the sum of Ahmed's age and Maria's age was 30. If Ahmed is now 3 times as old as Maria, find their current ages.
3. Sarah is currently twice as old as her brother, Alex. The sum of their ages is 45. Find the age of each sibling.
4. Ten years ago, the sum of Olivia's age and Peter's age was 50. If Olivia is now three times as old as Peter, find their current ages.
5. The sum of three consecutive odd integers is 99. Find the integers.
6. Mark is twice as old as his brother, Jake. The sum of their ages is 36. Determine the age of each.
7. Five years ago, the sum of Angela's age and Kevin's age was 45. If Angela is now four times as old as Kevin, find their current ages.
Section 2: Consecutive Numbers-Based Questions
8. Find three consecutive integers such that the sum of the first and third integers is 42.
9. Four consecutive integers have a product of 210. Find the integers.
10. The sum of three consecutive multiples of 5 is 105. Find the multiples.
11. The sum of three consecutive square numbers is 122. Find the numbers.
12. Find three consecutive even integers such that the sum of the squares of the first two integers is 365.
Section 3: Better Plan-Based Questions
13. Two mobile phone plans are available:
- Plan A costs $30 per month plus $0.05 per minute of talk time.
- Plan B costs $20 per month plus $0.08 per minute of talk time.
Determine the number of minutes of talk time for which both plans cost the same.
14. Two internet plans are available:
- Plan C: $40 per month plus $0.10 per gigabyte.
- Plan D: $30 per month plus $0.15 per gigabyte.
Determine the amount of data usage for which both plans cost the same.
15. A shipping company offers two plans:
- Plan M: $15 per package plus $2 per pound for shipping.
- Plan N: $10 per package plus $3 per pound for shipping.
Determine the weight of a package for which both plans cost the same.
16. Sam and Lisa are planning a trip. Sam's plan costs $50 per night plus $20 per person, while Lisa's plan costs $40 per night plus $25 per person. Determine the number of people for which both plans cost the same.
17. Three friends are considering different internet plans:
- Plan X: $35 per month plus $0.12 per gigabyte.
- Plan Y: $25 per month plus $0.18 per gigabyte.
Determine the amount of data usage for which both plans cost the same.
Section 4: Length and Width-Based Questions
18. The length of a rectangle is 4 cm more than twice its width. If the perimeter of the rectangle is 48 cm, find the length and width.
19. The length of a rectangular field is three times its width. If the area is 240 square meters, find the length and width.
20. The perimeter of a rectangle is 36 cm. If the length is twice the width, find the length and width.
21. The length of a rectangular room is 7 meters more than its width. If the area is 120 square meters, find the length and width.
Bonus Challenge: Triangular Garden
A triangular garden has a perimeter of 45 meters. If one side is 5 meters longer than the second side, and the third side is twice the length of the second side, find the lengths of all three sides.