Question

The coffee Lily likes is composed of 97.3% water and 2.7% cocoa. The coffee John likes is composed of 96% water and 4% cocoa. How many ounces of water, x, should be added to 30 ounces of coffee that John likes to make the coffee that Lily likes?

Answer 1

30 ounces of the coffee John likes consists of

• 
  `0.96\cdot30=28.8` ounces of water
• 
  `0.04\cdot30=1.2` ounces of cocoa

To this mixture we're adding
`x` ounces of water, so that the new mix has a total volume of
`30+x` ounces and matches the composition of the coffee Lily likes. This means it would consist of

• 
  `0.973\cdot(30+x)=28.8+x` ounces of water
• 
  `0.027\cdot(30+x)=1.2` ounces of cocoa (same amount of cocoa as before because pure water is being added)

Solve for
`x`:

`0.973(30+x)=28.8+x\implies29.12+0.973x=28.8+x`

`\implies0.39=0.027x`

`\implies x\approx14.4`

###

Just to confirm: the new mixture consists of

• 
  `28.8+14.4=43.2` ounces of water
• 
  `1.2+0=1.2` ounces of cocoa

giving a total volume of
`43.2+1.2=44.4` ounces of coffee, and
`(43.2)/(44.4)\approx0.973`, as required.