A crate contained forks and knives. \( {3 \over 5}{}{}\) of the cutlery in the crate were forks. 30 forks and 4 knives were removed from the crate and the remaining cutlery were divided into groups of 9 pieces each. In each group, there were 5 forks. What is the total number of cutlery in the crate at first?

Whayousayy Sep 9, 2021

#1**+2 **

A crate contained forks and knives. 3/5 of the cutlery in the crate were forks. 30 forks and 4 knives were removed from the crate and the remaining cutlery were divided into groups of 9 pieces each. In each group, there were 5 forks. What is the total number of cutlery in the crate at first?

Let there by F forks and K knives and a total of T pieces of cutlery

_{"A crate contained forks and knives. 3/5 of the cutlery in the crate were forks."}

so F= 0.6T and K=0.4T

_{30 forks and 4 knives were removed from the crate}

So the number of forks left is 0.6T - 30

and the number of knives left is 0.4T - 4

Now there are divided into groups of 9 Every group has 5 forks and therefore every group must have 4 knives.

The ratio of forks to knives (that are remaining) must be 5:4

so

\(\frac{0.6T-30}{0.4T-4}=\frac{5}{4}\\ 2.4T-120=2T-20\\ 0.4T=100\\ T=250\)

Melody Sep 11, 2021