Question

1/4 of the roses are red, 1/3 of the remainder are yellow and the rest are pink. There are 24 more pink roses than red roses. How many roses are there altogether?

Answer 1

There are 96 roses altogether

Solution:

Let "x" be the number of roses

From given,

1/4 of the roses are red

`Red\ roses = (1)/(4) * x\\\\Red\ roses = (x)/(4)`

1/3 of the remainder are yellow

`Remaining = x - (x)/(4)\\\\Remaining = (3x)/(4)`

Therefore,

`Yellow\ roses = (1)/(3) * (3x)/(4)\\\\Yellow\ roses = (x)/(4)`

Rest are pink

`Remaining = (3x)/(4) - (x)/(4)\\\\Remaining = (2x)/(4)\\\\Remaining = (x)/(2)`

Therefore,

`Pink\ Roses = (x)/(2)`

There are 24 more pink roses than red roses

Therefore,

Number of pink roses = 24 + red roses

`(x)/(2) = 24 + (x)/(4)\\\\(x)/(2) - (x)/(4) = 24\\\\(x)/(4) = 24\\\\x = 24 * 4\\\\x = 96`

Thus there are 96 roses altogether