Answer: 3 blue buckets and 4 white buckets were purchased.
Step-by-step explanation:
Let x represent the number of blue buckets that were purchased.
Let y represent the number of white buckets that were purchased.
The local hardware store has blue buckets that hold 2 gallons of water and white buckets that hold 5 gallons of water. The buckets that you bought can hold 26 gallons of water. This means that
2x + 5y = 26 - - - - - - - - - - - - -1
The number of buckets that you bought is 7. This means that
x + y = 7
Substituting x = 7 - y into equation 1, it becomes
2(7 - y) + 5y = 26
14 - 2y + 5y = 26
- 2y + 5y = 26 - 14
3y = 12
y = 12/3
y = 4
x = 7 - y = 7 - 4
x = 3
