Question

The container that holds the water for the football team is

2/5 full. After pouring in 8 gallons of water, it is 2/3
full. How many gallons can the container hold?

Answer 1

so, the container was 2/5 full
someone came over and dumped a bucket of water in it with 8 gallons
and the container went UP to 2/3 full

so, 8 gallons, and the container goes up by some fraction,
whatever that is

bear in mind that, 2/3 is over 1/2, and 2/5 is less than 1/2
so, 2/3 is really more than 2/5

so... whatever 8 gallons is in fraction of the container,
is the difference of 2/3 and 2/5
so.. let's say the container when full holds "x" amount of gallons
2/5 of x is... well, 2x/5
and 2/3 of x is well, 2x/3
so... we could say that
`8=\cfrac{2}{3}x-\cfrac{2}{5}x\implies 8=\cfrac{2x}{3}-\cfrac{2x}{5}`

solve for "x", since "x" is how many gallons, the container holds when full