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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 :

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:

[tex]\frac{3}{4}\colon4[/tex]

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:

[tex]\begin{gathered} \frac{3}{4}\colon4 \\ 116\colon x \\ \text{Cross multiply, we have:} \\ \frac{3}{4}x=116\cdot4 \\ 3x=116\cdot4\cdot4 \\ x=\frac{116\cdot4\cdot4}{3}=\frac{1856}{3} \\ x=618\frac{2}{3} \end{gathered}[/tex]

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

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