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:
[tex]x = 72[/tex]
Step-by-step explanation:
Let:
[tex]D = Dominic;\ \ S = Sarah;\ \ P = Piper;\ \ V = Vaughn[/tex]
From the [rephrased] question, we have:
[tex]D = S - 15[/tex]
[tex]S = 12 + P[/tex]
[tex]P = \frac{1}{4}V[/tex]
[tex]V = 9 + D + S + P[/tex]
Substitute [tex]S = 12 + P[/tex] in [tex]D = S - 15[/tex]
[tex]D = 12 + P - 15[/tex]
[tex]D = P+12 - 15[/tex]
[tex]D = P-3[/tex]
Make V the subject in [tex]P = \frac{1}{4}V[/tex]
[tex]V = 4P[/tex]
Substitute: [tex]V = 4P[/tex], [tex]D = P-3[/tex] and [tex]S = 12 + P[/tex] in [tex]V = 9 + D + S + P[/tex]
[tex]4P= 9 + P - 3 + 12 + P +P[/tex]
Collect like terms
[tex]4P - P -P-P= 9 - 3 + 12[/tex]
[tex]P= 18[/tex]
Substitute [tex]P= 18[/tex] in [tex]S = 12 + P[/tex]
[tex]S = 12 +18[/tex]
[tex]S = 30[/tex]
Substitute [tex]S = 30[/tex] in [tex]D = S - 15[/tex]
[tex]D = 30 - 15[/tex]
[tex]D =15[/tex]
Substitute [tex]D =15[/tex], [tex]S = 30[/tex] and [tex]P= 18[/tex] in [tex]V = 9 + D + S + P[/tex]
[tex]V = 9 + 15 + 30 + 18[/tex]
[tex]V = 72[/tex]
x represents the number collected by Vaughan.
So:
[tex]x = 72[/tex]
