Question

a punch recipe calls for orange juice and ginger ale in the ratio 2/3:1/4. if kyle made 22 cups of punch how many cups of each ingredient did he use?

Answer 1

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

`\begin{gathered} (2)/(3)x\text{ +}(1)/(4)x\text{ = 22} \\ \text{ The common denominator = 3 x 4} \\ Common\text{ denominator = 12} \\ \frac{12\frac{2x\text{ }}{3}\text{ + 12}(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} \\ (11x)/(11)\text{ = }(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} \\ (2)/(3)x \\ x\text{ = 24} \\ \text{Cup of orange juice = }(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} \\ (1)/(4)\text{ x 24} \\ =\text{ 6 cups} \\ \text{Therefore, 6 cups of ginger ale was used} \end{gathered}`