Question

A pitcher of water is three-fourths full. Four cups of water are served from the pitcher. Then the pitcher is two-thirds full. How many cups of water can the pitcher hold?

Answer 1

so hmmm let's say, the pitcher has "x" cups when full
so, it was (3/4)x then 4 cups came out, went down to (2/3)x

now, if we subtract (2/3)x from (3/4)x, their difference will be the 4cups that were served

thus
`\bf \cfrac{3}{4}x-\cfrac{2}{3}x=4\implies \cfrac{3x}{4}-\cfrac{2x}{3}=4\implies \cfrac{3\cdot 3x-4\cdot 2x}{12}=4 \\\\\\ \cfrac{9x-8x}{12}=4\implies \cfrac{x}{12}=4`

and surely, you'd already know what "x" is