ANSWER
Marty filled 8 buckets of water
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:
[tex]y=10x[/tex]And that Melissa filled 6 times as many buckets as Marty:
[tex]z=6x[/tex]All three of them together fulled 136 buckets:
[tex]x+y+z=136[/tex]Replace y and z as functions of x:
[tex]x+10x+6x=136[/tex]And solve for x. First add like terms:
[tex]\begin{gathered} (1+10+6)x=136 \\ 17x=136 \end{gathered}[/tex]And divide both sides by 17:
[tex]\begin{gathered} \frac{17x}{17}=\frac{136}{17} \\ x=8 \end{gathered}[/tex]We found that Marty filled 8 buckets of water.
