Question

EXPRESSION1)A punch recipe requires 2 cups of cranberry juice to make 3 gallons of punch. Using the same recipe, what is the amount of cranberry juice needed for 1 gallon of punch? Please show me how you got your answer.2)A HIGH-SPEED ELEVATOR CAN RISE 480 FT IN 30 SEC, WHICH EXPRESSION REPRESENTS THE RATE. IN FT PER MIN, OF THE ELEVATOR

Answer 1

Step 1

Given;

`2\text{ cups of cranberry juice - 3 gallons of punch}`

Required; To find the amount of cranberry juice required for 1 gallon of punch juice.

Step 2

So basically, you can set this up in proportion.

For every gallon of punch, 2 cups of cranberry juice is needed. What you need to find is the amount of cranberry juice is needed for one gallon. So then you would have to set up your proportion like this:

`\begin{gathered} \frac{2\text{ cups of cranberry juice}}{\text{3 gallons of punch}}=\frac{x\text{ cups of cranberry juice}}{1\text{ gallon of punch}} \\ or \\ (2)/(3)=(x)/(1) \end{gathered}`

We will now find the value of x by cross multiplying

`\begin{gathered} 2*1=3* x \\ 2=3x \\ (3x)/(3)=(2)/(3) \\ x=(2)/(3) \end{gathered}`

So you will need 2/3 cups of cranberry juice for 1 gallon of punch

Answer;

`(2)/(3)\text{ cups of cranberry juice}`

Step 3

2) The elevator rises 480ft in 30 seconds

One minute=60 seconds.

Therefore, we will have;

`\begin{gathered} \frac{480ft}{\text{xft}}=\frac{30\sec onds}{1\text{ minute}} \\ 1\text{ minute=60 seconds} \\ \frac{480ft}{\text{xft}}=\frac{30\sec onds}{60\text{ seconds}} \\ or \\ (480)/(x)=(30)/(60) \\ (480)/(x)=(1)/(2) \\ \end{gathered}`
`\begin{gathered} x=480*2 \\ x=960ft\text{ per second} \end{gathered}`