Question

A water tank contains 6500 litre of water. during transit to a nearby society, 3 by 16 of the water was spilt. find the volume of water in the tank that finally reached the society.​

Answer 1

Answer:

A tank is 2/3 full of water, when 1/8 of the water in the tank was drawn, 2800 litres remained. What is the capacity of the tank?

Imo these problems are worked from the inside out. Meaning, you're left with 2800 litres. That's something you factually know.

2800 litres

We're also told where it comes from. It's what's left after 1/8 of water of the tank is removed. Or also, when 7/8 of the water is left of what started in the tank.

So, now we're given info to find the amount of water the tank had before we removed 1/8 of it. The amount of water is unknown, and that's what our first variable, x, will be.

So to get the amount of water, we're left with:

2800 litres is 7/8 of the water . To find the amount of water we had to start with, before taking anything out, we have:

2800 = 7/8x

From here, we divide both sides of our equation by 7/8. This results in:

2800/(7/8) = (7/8)/(7/8) * x

This is okay to do because as long as we're performing the same operation with the same values on both sides of the equation, it's still a true statement.

Due to how division works, we can rewrite the left hand side above as:

2800 * (1 / (7/8))

Which is equal to

2800 * (8/7)

Which equates to 3200.

Do the same for the right hand side

7/8 * (8/7) * x => 1 * x => x

And voila we're left with 3200 = x.

Remember, this x we defined was the total amount of water we started with in the tank, in litres, since the units we used in our calculations were litres.

However, the amount of water we initially had in the tank was 2/3 the entire capacity of the tank. The capacity of the tank is unknown, but now we have knowledge of the amount of water inside the tank!

Thus, we'll name our new unknown as any variable, let's call it t.