Question

Mrs Allen gave some peanuts to her children to take to the zoo. Zach got half the peanuts, Wendy got one-fourth of what was left. The twins, Ron and don shared the remaining peanuts. If Ron got 45 peanuts, how many peanuts did Mrs Allen give to her children

Answer 1

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 $\dfrac{x}{2}$ peanuts and

$x-\dfrac{x}{2}=\dfrac{x}{2}$ peanuts left.

Wendy got one-fourth of what was left, then Wendy got

$\dfrac{1}{4}\cdot \dfrac{x}{2}=\dfrac{x}{8}$ peanuts and

$\dfrac{x}{2}-\dfrac{x}{8}=\dfrac{3x}{8}$ peanuts left.

The twins, Ron and Don shared the remaining peanuts, then each of them got

$\dfrac{1}{2}\cdot \dfrac{3x}{8}=\dfrac{3x}{16}$ peanuts.

If Ron got 45 peanuts, then

$\dfrac{3x}{16}=45,\\ \\3x=45\cdot 16,\\ \\x=15\cdot 16,\\ \\x=240\ \text{peanuts.}$