Question

Debby filled 10 times as many buckets of water as Marty, and Melissa filled 6 times as many buckets as Marty. All

3 together filled 136 buckets of water to fill a pool. How many buckets did Marty fill?

Answer 1

Marty filled 8 buckets of water

Step-by-step explanation

Let

• x: number of buckets Marty filled

,

• y: number of buckets Debby filled

,

• z: number of buckets Melissa filled

We know that Debby filled 10 times as many buckets as Marty:

`y=10x`

And that Melissa filled 6 times as many buckets as Marty:

`z=6x`

All three of them together fulled 136 buckets:

`x+y+z=136`

Replace y and z as functions of x:

`x+10x+6x=136`

And solve for x. First add like terms:

`\begin{gathered} (1+10+6)x=136 \\ 17x=136 \end{gathered}`

And divide both sides by 17:

`\begin{gathered} (17x)/(17)=(136)/(17) \\ x=8 \end{gathered}`

We found that Marty filled 8 buckets of water.