Question

Mr Ang had a total number of 384 buns in 2 shops, \(K\) and L. After he transferred 60 buns from Shop \(L\) to Shop K, Shop K had 7 times as many buns as Shop L. How many buns were there in Shop K at first?

Answer 1

\(x=283.5\) and \(y=100.5\)

 

Explanation:

Let \(x\) be the number of buns in shop \(K\) and let \(y\) be the number of buns in shop in \(L\)

Since the total number of buns fromthe two shops is 384, then:

\[x+y=384\]

Given that after moving 60 buns, shop \(K\) now has 7 times more than \(L\) so:

\[x=7(y-60)\]

\[x-7y=-420\]

Now we have the simultaneous equations:

\[x+y=384 \]

\[x-7y=-420\]

 

Subtracting the second equation from the first eliminates \(x\)

\[8y=804\]

\[y=100.5\]

substituting for \(y\) gives:

\[x+100.5=384 \]

\[x=283.5\]