Question

A milk boy sold milk in packets of 250 ml and 500 ml. He sold 6 L of milk in 17 packets. How many packets of each type did he sell?

Answer 1

Hint: Let x be the number of packets of 250 ml milk capacity. So, the number of 500 ml packets sold will be \[\left( {17-x} \right)\] .
It is given that he sold 6 L = 6000 ml milk in total. So, the sum of the capacity of milk sold in 250 ml packets and capacity of milk sold in 500 ml packets will be equal to 6000.
By forming a linear equation using the above information, find x, where x will be the number of packets of 250 ml milk. Now, substitute x in \[\left( {17-x} \right)\] to get the number of packets of 500 ml milk sold.

Complete step-by-step answer:
It is given that a milk boy sold milk in packets of 250 ml and 500 ml.
Let x be the number of packets of 250 ml milk capacity.
Also, he sold 17 packets of milk in total.
Thus, the number of packets of 500 ml capacity is \[\left( {17-x} \right)\] .
Thus, the capacity of milk sold in 250 ml packets will be 250x and the capacity of milk sold in 500 ml packets will be 500 \[\left( {17-x} \right)\] .
He sold a total 6 L = 6000 ml of milk.
So, the sum of the capacity of milk sold in 250 ml packets and capacity of milk sold in 500 ml packets will be equal to 6000.
 $\Rightarrow 250x + 500\left( {17-x} \right) = 6000$
 $\Rightarrow 250x + 8500-500x = 6000$
 \[\Rightarrow 8500-6000 = 250x\]
 \[\Rightarrow 250x = 2500\]
  $\Rightarrow x = 10$ .
Thus, the number of packets of 250 ml milk sold is 10.
So, the number of packets of 500 ml milk sold is \[\left( {17-10} \right)\] = 7.

Note: Alternate Method:
It is given that a milk boy sold milk in packets of 250 ml and 500 ml.
Let x be the number of packets of 250 ml capacity of milk and y be the number of 500 ml capacity of milk.
Also, given that, he sold 17 packets in total.
 $\therefore x + y = 17$ ... (1)
Thus, the capacity of milk sold in 250 ml packets will be 250x and capacity of milk sold in 500 ml packets will be 500y.
Also, the capacity of milk sold is 6 L = 6000 ml.
 $\Rightarrow 250x + 500y = 6000$
 $\Rightarrow 250\left( {x + 2y} \right) = 6000$
 $\Rightarrow x + 2y = 24$ ... (2)
Now, from equation (1) we get \[x = 17-y\] .
Substituting \[x = 17-y\] in equation (2) will give
 \[17-y + 2y = 24\]
 $\Rightarrow y = 24-17$
 $\Rightarrow y = 7$
Thus, we get \[y = 7\] .
Substituting \[y = 7\] in equation (1) will give
 \[x + 7 = 17\]
 $\Rightarrow x = 17-7$
 $\Rightarrow x = 10$
So, \[x = 10\] and \[y = 7\] .
Thus, the number of packets of 250 ml milk sold is 10 and the number of packets of 500 ml milk sold is 7.