Question

Mary had flowers, of which 3/5 were roses and the rest were orchids. She sold 1/2 of the roses and 1/4 of the orchids. She then had 54 roses and orchids left. How many flowers did she have at first?

Answer 1

Mary have 90 flowers

Explanation:

Given that Mary had flowers, of which 3/5 were roses and the rest were orchids.

Let Mary had x flowers.

∴ Roses are=
`(3)/(5) x`

and orchids are
`x-(3)/(5)x=(2)/(5)x`

Now, She sold 1/2 of the roses and 1/4 of the orchids. She then had 54 roses and orchids left.

Hence, total flowers i.e roses and orchids sold are
`(1)/(2)((3)/(5)x)+(1)/(4)((2)/(5)x)=(4)/(10)x=(2)/(5)x`

The flowers which left are
`x-(2)/(5)x=(3)/(5)x`

⇒
`(3)/(5)x=54`⇒
`x=90`

Therefore, Mary have 90 flowers