Question

6. There are 30 students in Mr. Jones’ fifth grade and 28 students in Mr. Smith’s fifth grade. They are planning a joint project and need 2 cups of juice per student for refreshments. If they mix ¾ cup juice concentrate to 4 cups of water, how many cups of juice concentrate and water do they need? (8 points)

Answer 1

Let's begin by listing out the information given to us:

number of students (Mr Jones) = 30

number of students (Mr Smith) = 28

2 cups of juice per student

¾ cup of juice = 4 cups of water

Ratio of cup of juice to cup of water is:

`(3)/(4)\colon4`

There are a total of 58 students. That means they will need 116 cups of juice (2 per person). We will get the cups of water needed by:

`\begin{gathered} (3)/(4)\colon4 \\ 116\colon x \\ \text{Cross multiply, we have:} \\ (3)/(4)x=116\cdot4 \\ 3x=116\cdot4\cdot4 \\ x=(116\cdot4\cdot4)/(3)=(1856)/(3) \\ x=618(2)/(3) \end{gathered}`

They need 116 cup of juice and 618 2/3 cups of water