There are four times as many roses as tulips in Claire’s garden. Claire picked half of the number of roses and 140 roses were left in the garden. How many roses and tulips were in the Garden the first?

Let's assume the number of tulips in Claire's garden is $x$.

According to the information given, there are four times as many roses as tulips. Therefore, the number of roses in the garden is $4x$.

Claire picked half of the number of roses, so she picked $\frac{1}{2}(4x) = 2x$ roses.

After Claire picked the roses, 140 roses were left in the garden. This means that $4x - 2x = 140$.

Simplifying the equation, we have $2x = 140$.

To find the value of $x$, we divide both sides of the equation by 2:

$\frac{2x}{2} = \frac{140}{2}$

$x = 70$

So, there were 70 tulips in the garden initially.

The number of roses in the garden is $4x = 4(70) = 280$.

Answer: There were 70 tulips and 280 roses in the garden initially.