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

Apr 3, 2015

The answer is: $15$

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

We know this:

$\frac{l}{r} = \frac{1}{3}$

So $3 l = r$

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

$l + 3 l = 20$

$4 l = 20$

$l = 5$

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

Apr 3, 2015

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:
$R = 3 L$

Let's substitute $R$ from our second equation into our first equation:
$L + \textcolor{red}{3 L} = 20$
$4 L = 20$
$L = 5$ There are 5 lilies.

Since $R = 3 L$ and $L = 5$:
$R = 3 \cdot \textcolor{red}{5}$
$R = 15$ There are 15 roses.