Answer:
240 peanuts
Step-by-step explanation:
Let x be the number of peanuts Mr. Allen had.
Zach got half the peanuts, then Zach got [tex]\dfrac{x}{2}[/tex] peanuts and
[tex]x-\dfrac{x}{2}=\dfrac{x}{2}[/tex] peanuts left.
Wendy got one-fourth of what was left, then Wendy got
[tex]\dfrac{1}{4}\cdot \dfrac{x}{2}=\dfrac{x}{8}[/tex] peanuts and
[tex]\dfrac{x}{2}-\dfrac{x}{8}=\dfrac{3x}{8}[/tex] peanuts left.
The twins, Ron and Don shared the remaining peanuts, then each of them got
[tex]\dfrac{1}{2}\cdot \dfrac{3x}{8}=\dfrac{3x}{16}[/tex] peanuts.
If Ron got 45 peanuts, then
[tex]\dfrac{3x}{16}=45,\\ \\3x=45\cdot 16,\\ \\x=15\cdot 16,\\ \\x=240\ \text{peanuts.}[/tex]