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?

Question

asked Oct 18, 2021 75.2k views

1 Answer

Kamal · Answer 1 · 2021-10-22T08:10:01+0000

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