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

240 peanuts

Explanation:

Let x be the number of peanuts Mr. Allen had.

Zach got half the peanuts, then Zach got
`(x)/(2)` peanuts and

`x-(x)/(2)=(x)/(2)` peanuts left.

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

`(1)/(4)\cdot (x)/(2)=(x)/(8)` peanuts and

`(x)/(2)-(x)/(8)=(3x)/(8)` peanuts left.

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

`(1)/(2)\cdot (3x)/(8)=(3x)/(16)` peanuts.

If Ron got 45 peanuts, then

`(3x)/(16)=45,\\ \\3x=45\cdot 16,\\ \\x=15\cdot 16,\\ \\x=240\ \text{peanuts.}`