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 $x$:

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

$\implies0.39=0.027x$

$\implies x\approx14.4$

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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 $\dfrac{43.2}{44.4}\approx0.973$, as required.