Question

For volunteers picked up letter from the park Dominic you collect and 15 for your pieces a litter than Sarah Sarah collect the 12 more pieces in piper piper collected 1/4 as many pieces of litter as Vaughn Vaughn has collected nine more pieces of wood or than everyone else combine the X represent the number of pieces of litter Vaughn Collection

Answer 1

So many confusing details. So, I rephrase the question as:

Four volunteers picked up litters from the park.

Dominic collect 15 pieces less than Sarah. Sarah collects 12 more pieces than Piper. Piper collected 1/4 as many pieces of letter as Vaughn. Vaughn has collected nine more pieces of letter than everyone else combined. Let x represent the number of pieces of litter in Vaughn's Collection. Find x

Answer:

`x = 72`

Explanation:

Let:

`D = Dominic;\ \ S = Sarah;\ \ P = Piper;\ \ V = Vaughn`

From the [rephrased] question, we have:

`D = S - 15`

`S = 12 + P`

`P = (1)/(4)V`

`V = 9 + D + S + P`

Substitute
`S = 12 + P` in
`D = S - 15`

`D = 12 + P - 15`

`D = P+12 - 15`

`D = P-3`

Make V the subject in
`P = (1)/(4)V`

`V = 4P`

Substitute:
`V = 4P`,
`D = P-3` and
`S = 12 + P` in
`V = 9 + D + S + P`

`4P= 9 + P - 3 + 12 + P +P`

Collect like terms

`4P - P -P-P= 9 - 3 + 12`

`P= 18`

Substitute
`P= 18` in
`S = 12 + P`

`S = 12 +18`

`S = 30`

Substitute
`S = 30` in
`D = S - 15`

`D = 30 - 15`

`D =15`

Substitute
`D =15`,
`S = 30` and
`P= 18` in
`V = 9 + D + S + P`

`V = 9 + 15 + 30 + 18`

`V = 72`

x represents the number collected by Vaughan.

So:

`x = 72`