Question

A store sells batteries in packets of 6 or 10. It has a stock of 25 packets containing a total of 186 batteries. How many of these are 10-battery packets?

Answer 1

Hello!

The answer is: There are 9 packets of 10-battery packets.

Why?

Let's make the calculations:

Let y b the 6-battery packet and z be the 10-battery packet.

We must construct the following to equations using the statement information: There is a stock of 25 packets and there is a total of 186 batteries formed by 6-battery packets and 10-battery packers

So, the first equation will be:

`y + z = 25`

The second equation will be:

`6y+10z=186`

From the first equation we have:

`y=25-z`

Substituting y in the second equation we have:

`6(25-z)+10z=186\\6(25-z)=186-10z\\150-6z=186-10z\\10z-6z=186-150\\4z=36\\z=(36)/(4)=9`

So, there are 9 packets of 10-battery packets.

By substituting z in the first equation we will know the number of 6-battery packets in stock

`y=25-9=16`

So, there are 16 packets of 6-battery packets.

Have a nice day!

Answer 2

9

Explanation:

Let the number of 10 battery packets is x

and the number of 6 packets battery is y

Now, it has been given that store has a stock of 25 packets. It means

`x+y=25\\y=25-x.......(1)`

Also, the number of batteries are 186. Thus, the equation is

`10x+6y=186`

Plugging the value of y from equation 1,

`10x+6(25-x)=186\\\\10x+150-6x=186\\\\4x=36\\\\x=9`

Hence, there are 9 ten-battery packets.