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

$Red\ roses = \frac{1}{4} \times x\\\\Red\ roses = \frac{x}{4}$

1/3 of the remainder are yellow

$Remaining = x - \frac{x}{4}\\\\Remaining = \frac{3x}{4}$

Therefore,

$Yellow\ roses = \frac{1}{3} \times \frac{3x}{4}\\\\Yellow\ roses = \frac{x}{4}$

Rest are pink

$Remaining = \frac{3x}{4} - \frac{x}{4}\\\\Remaining = \frac{2x}{4}\\\\Remaining = \frac{x}{2}$

Therefore,

$Pink\ Roses = \frac{x}{2}$

There are 24 more pink roses than red roses

Therefore,

Number of pink roses = 24 + red roses

$\frac{x}{2} = 24 + \frac{x}{4}\\\\\frac{x}{2} - \frac{x}{4} = 24\\\\\frac{x}{4} = 24\\\\x = 24 \times 4\\\\x = 96$

Thus there are 96 roses altogether