Question

The local hardware store has blue buckets that hold 2 gallons of water and white buckets that hold 5 gallons of water. You bought 7 buckets that can hold 26 gallons of water. How many buckets of each color were purchased?

Answer 1

So 3 blue buckets and 4 white buckets were purchased

Explanation:

We can solve this by algebra

Let B = number of blue buckets bought

Let W = number of white buckets bought

Total buckets bought:
B + W = 7 (1)

Each blue bucket can hold 2 gallons of water
So B blue buckets can hold 2B gallons of water

Each white bucket can hold 5 gallons of water
So W white buckets can hold 5W gallons of water

Totally they can hold
2B + 5W gallons

We are given that they both can hold 26 gallons of water

So our second equation is
2B + 5W = 26 (2)

By eliminating one of the variable terms we can solve for the other variable term

Let's eliminate the term for variable B

Multiply equation (1) by 2

(1) x 2 ==> 2(B + W) = 2(7)

2B + 2W = 14 (3)

Subtract (3) from (2); B terms are same so they cancel out

(2) - (3):
2B + 5W = 26
`\bold{-}`
2B + 2W = 14
---------------------
0 + 3W = 12
------------------------

3W = 12
W = 12/3

W = 4

Substitute W= 4 in equation 1
B + W = 7
=> B + 4 = 7

B = 3

So 3 blue buckets and 4 white buckets were purchased