Algebra Garden




Algebra Garden

All measurements in this problem are counting numbers.

A square garden contains a variety of different plants, all of which are thriving in an award winning environment.
The sidewalk on each side of the square garden is a different width.
There is a sundial in the middle of the narrowest walk.
The next widest sidewalk is a foot wider than the sundial side.
The next widest sidewalk after that one is 2 feet wider than the sundial side.
The final sidewalk is 3 feet wider than the sundial side.
The outside edges of the walk form a square.
The lot that contains the garden and sidewalks is a square.
If the area of the lot is 621 square feet greater than that of the garden, how wide is the sidewalk on the side of the garden opposite the walk containing the sundial?


Correct Solutions:


  1. Teddy Schaffer. Westminster Schools, Atlanta, GA
  2. Justin Lam. College Park HS, Pleasant Hill, CA
  3. Wojciech Lewkowicz. Lemont HS, Lemont, IL
  4. Alex Lorbert. Yeshivah of Flatbush HS, Brooklyn, NY
  5. Catherine Harrison. The Mount School, York, England, UK
  6. Sarah Buchanan. The Mount School, York, England, UK
  7. Becci Johnson. The Mount School, York, England, UK
  8. Kittie Jones. The Mount School, York, England, UK
  9. Jenny Scott. The Mount School, York, England, UK
  10. Jian Wu. The Mount School, York, England, UK
  11. Alice Wishart. The Mount School, York, England, UK
  12. Clare Hatfield. The Mount School, York, England, UK
  13. Sarah Halford-Fletcher. The Mount School, York, England, UK
  14. Anna Casson. The Mount School, York, England, UK
  15. Emma Hardwick. The Mount School, York, England, UK
  16. Craig Chasseur. Center For Arts & Science, Saginaw, MI
  17. Chris Young. Center For Arts & Sciences, Saginaw, MI
  18. Alan Zebchuk. St. Mark Catholic HS, Manotick, Ontario, Canada
  19. Shannon Ingram. Walkersville HS, Walkersville, MD
  20. Angela Farrell. Sauk Centre HS, Sauk Centre, MN
  21. Christopher Coyle. Msgr. Donovan HS, Toms River, NJ
  22. Sean Kody. Msgr. Donovan HS, Toms River, NJ
  23. Paul Pagano. Msgr. Donovan HS, Toms River, NJ
  24. Paul Gardner. Msgr. Donovan HS, Toms River, NJ
  25. Ashley Holifield. Jackson Prep JHS, Jackson, MS
  26. Rachel Olson. Douglas HS, Winston, OR
  27. Erin Perkins. Lake Highland Prep, Orlando, FL
  28. Chris Cunningham. Center for Arts & Sciences, Saginaw, MI
  29. Patrick McHenry. Oviedo HS, Oviedo FL
  30. Katie Wagner. McRoberts Secondary, Richmond, BC, Canada
  31. Michael Moyer. The Way Home School, Carlisle, PA