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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?

 Sep 9, 2021
 #1
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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

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

 Sep 11, 2021

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