Answer :
Answer: Orange juice = 16 cups
Ginger ale = 6 cups
Punch recipe contains orange and ginger ale in the ratio of
2/3 : 1/4
Kyle made a 22 cups of punch
We will be using a single variable expression to find the cup of each ingredient
Orange + ginger ale = punch
Let x be the number of orange and ginger ale
For every 2/3 of range juice we have 1/4 of giner ale
[tex]\begin{gathered} \frac{2}{3}x\text{ +}\frac{1}{4}x\text{ = 22} \\ \text{ The common denominator = 3 x 4} \\ Common\text{ denominator = 12} \\ \frac{12\frac{2x\text{ }}{3}\text{ + 12}\frac{x}{4}}{12}\text{ = 22} \\ \frac{4(2x)\text{ + 3(x) }}{12}\text{ = 22} \\ \frac{8x\text{ + 3x}}{12}\text{ = 22} \\ \text{Cross multiply} \\ 11x\text{ = 22 x 12} \\ 11x\text{ = 264} \\ \text{Divide both sides by 11} \\ \frac{11x}{11}\text{ = }\frac{264}{11} \\ x\text{ = 24} \\ \text{ Since, he used 2/3 of orange juice} \\ \text{Hence, the cup of orange juice can be calculated as follows} \\ \frac{2}{3}x \\ x\text{ = 24} \\ \text{Cup of orange juice = }\frac{2}{3}\text{ x 24} \\ =\text{ 2 x 8} \\ =\text{ 16 cups} \\ \text{Therefore, 16 cups of orange juice was used.} \\ \text{For ginger ale} \\ \frac{1}{4}\text{ x 24} \\ =\text{ 6 cups} \\ \text{Therefore, 6 cups of ginger ale was used} \end{gathered}[/tex]