Let
x=no. Of shuttlecocks
y= no. of cricket balls
Then eqn 8x+15y=769
Dividing eqn by 8 we get
Rem(8x+15y/8)=rem(769/8)
=>Rem(7y/8)=1
By trial ,y=7 satisfies the above condition and the other values of y can be obtained by adding 8 successively
y=7,15,23,31,39,47,55
But for y>=55,15y>769.
So y <55
The corresponding values of x are 83 ,68,53,38,23,8.
Hence the irems can be purchased in 6.