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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?

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LammettHash

30 ounces of the coffee John likes consists of

  • [tex]0.96\cdot30=28.8[/tex] ounces of water
  • [tex]0.04\cdot30=1.2[/tex] ounces of cocoa

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

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

Solve for [tex]x[/tex]:

[tex]0.973(30+x)=28.8+x\implies29.12+0.973x=28.8+x[/tex]

[tex]\implies0.39=0.027x[/tex]

[tex]\implies x\approx14.4[/tex]

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Just to confirm: the new mixture consists of

  • [tex]28.8+14.4=43.2[/tex] ounces of water
  • [tex]1.2+0=1.2[/tex] ounces of cocoa

giving a total volume of [tex]43.2+1.2=44.4[/tex] ounces of coffee, and [tex]\dfrac{43.2}{44.4}\approx0.973[/tex], as required.

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