Rachel planted a flower garden. She planted roses in 1/4 of the garden and 1/3 of the roses were pink. She planted tulips in 1/3 of the garden and 1/3 of the tulips were pink. How many roses were there in Rachel's garden?
To find out how many roses there were in Rachel's garden, we need to calculate the fraction of her garden that was planted with roses and then the fraction of those roses that were pink.
First, let's calculate the fraction of the garden that was planted with roses. We are given that roses were planted in 1/4 of the garden, so this means that 1/4 of the garden is made up of roses.
Next, let's calculate the fraction of the roses that were pink. We are given that 1/3 of the roses were pink, so this means that out of the 1/4 fraction of the garden that is roses, 1/3 of that fraction were pink.
To find out how many roses were in Rachel's garden, we need to multiply the fraction of the garden that is roses (1/4) by the fraction of those roses that are pink (1/3).
(1/4) * (1/3) = 1/12
So, 1/12 of Rachel's garden was planted with pink roses.
Since we know that 1/12 of the garden was planted with pink roses, we can find the total number of roses in the garden by dividing the fraction of roses by the fraction of pink roses:
1 / (1/12) = 12
Therefore, there were 12 roses in Rachel's garden.