Question

If there are 20 flowers, how many roses are there if bunches of Flowers have lillies and roses in the ratio 1:3?

Answer 1

The answer is: `15`

Lets say that there are `l` lillies and `r` roses.

We know this:

`l/r=1/3`

So `3l = r`

Also we know that `l+r=20`. We now know that `r=3l` then we can rewrite the equality as:

`l+3l=20`

`4l=20`

`l=5`

So if there are `5` lilies then there must be `15` roses.

Answer 2

Assuming the ratio is Lily : Rose , there are `5` lilies to `15` roses:

We know that there are `20` flowers in all, lilies and roses combined.
`L + R = 20`

We know that there are `3` times as many roses as there are lilies:
`R = 3L`

Let's substitute `R` from our second equation into our first equation:
`L + color(red)(3L) = 20`
`4L = 20`
`L = 5` There are 5 lilies.

Since `R = 3L` and `L=5`:
`R = 3*color(red)(5)`
`R = 15` There are 15 roses.

I hope that was helpful.