Question

The total cost of $8$ buckets and $5$ mugs is $Rs92$ and the total cost of $5$ buckets and $8$ mugs is $Rs77$. Find the cost of $2$ mugs and $3$ buckets

Answer 1

Let the cost of a bucket be $Rsx$ and that of a mug be $Rsy$. We have two equations:
$8x+5y=92,\left(1\right)$
$5x+8y=77.\left(2\right)$
Multiply the equation $\left(1\right)$ by $8$ and the equation $\left(2\right)$ by $5$, you get
$64x+40y=736$
$25x+40y=385$.
Subtracting the second from the first, we get $39x=351$. Thus we obtain $x=9$.
Putting this in the equation $\left(1\right)$, we get
$5y=92-8x=92-8\left(9\right)=92-72=20$.
We obtain $y=4$
Thus the cost of a bucket is $Rs9$ and that of a mug is $Rs4$.
Now the cost of $3$ buckets is $3\times 9=27$ rupees and that of $2$ mugs is $2\times 4=8$ rupees. The total cost is $Rs35$.