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Priya mixes [tex]2 \frac{1}{2} [/tex] cups of water with 1/3 cup of orange juice concentrate. Diego mixes 1 2/3 cups of water with 1/4 cup orange juice concentrate. how much concentrate should each of the mix with 100 cups of water to make juice that taste the same as their original recipe? explain or show your reasoning Create an an equation to show the amount of water and the amount of orange juice each person uses.

Answer :

Priya mixes : 2 1/2 cups of water with 1/3 cup of orange juice concentrate.

Diego mixes 1 2/3 cups of water with 1/4 cup orange juice concentrate.

So, to get the same taste with 100 cups for each recipe,

let the number of cubs of orange = x

for Priya mixes:

[tex]\begin{gathered} 2\frac{1}{2}\colon\frac{1}{3}=100\colon x \\ \\ \frac{5}{2}\colon\frac{1}{3}=100\colon x \\ \end{gathered}[/tex]

Solve for x:

[tex]\begin{gathered} \frac{\frac{5}{2}}{\frac{1}{3}}=\frac{100}{x} \\ \frac{5\cdot3}{2\cdot1}=\frac{100}{x} \\ \\ x=\frac{2\cdot100}{5\cdot3}=\frac{200}{15}=13\frac{1}{3} \end{gathered}[/tex]

So, Priya will need 13 1/3 cubs of orange

And for Diego mix:

[tex]1\frac{2}{3}\colon\frac{1}{4}=100\colon x[/tex][tex]\begin{gathered} \frac{5}{3}\colon\frac{1}{4}=100\colon x \\ \end{gathered}[/tex]

solve for x:

[tex]\begin{gathered} \frac{\frac{5}{3}}{\frac{1}{4}}=\frac{100}{x} \\ \\ \frac{5\cdot4}{1\cdot3}=\frac{100}{x} \\ \\ x=\frac{1\cdot3\cdot100}{5\cdot4}=\frac{300}{20}=15 \end{gathered}[/tex]

So, Diego will need 15 cubs of orange

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