Question

A manufacturer packages soap powder in containers of three different sizes. The amount of soap powder in a full large container could fill exactly 3 of the medium containers or exactly five of the small containers. If an equal number of large and small containers are to be filled with the amount of soap powder that would fill 90 medium containers, how many small containers would be filled?

Answer 1

Given that the large container can contain amount which can be filled in 3 medium containers or 5 small containers
So Let's say that the volume of large container be L, medium be M and small be S
so
We have
\[L=3M\]
\[L=5S\]
Do you agree with this?

Answer 2

Yes I do. But let's say the amount that can be filled in a large container is \[x] so is x = 3x correct?

Answer 3

No no it wont be, x cannot equal 3x. I got it. Yes, I agree to what you said L= 3 M and L = 5S

Answer 4

It's given that we have amount= 90M
Now we need to fill that in equal no. of large and small containers.
Do you get this?

Answer 5

Yes.

Answer 6

Suppose I have n no. of Large and small containers
so
\[nL+nS=90 M\]
Do you get this?

Answer 7

Why is it equal to the amount?

Answer 8

Why is it equal to the amount of soap powder?

Answer 9

We have to fill the amount in 90 medium containers in equal no. of small and large containers
Here I chose n large containers and n small containers. So the total amount of soap in n large and n small containers =
\[n\times L+n\times S\]
and this according to the condition given is equal to amount in 90 medium containers
\[n\times L+ n\times S=90M\]

Answer 10

Oh right!

Answer 11

Yes, I got it!

Answer 12

Now L=3M and L=5S
\[nL+nS=90M\]
Writing in terms of L
\[nL+n \frac L 5=90 \frac L 3\]
Dividing both sides by L
\[n+\frac n 5= \frac {90} 3\]
I think you can find n now, Can't you?

Answer 13

@Zeerak I'm going for some time. If you need help, let me know. I'll come back and help you out

Answer 14

n = 25.

Answer 15

Thank you so very much.