RP2

RP2

RP.2 Unit Rates and Proportions

Several friends meet at a coffee shop. They order 5 ice coffees and 3 frappuccinos and pay a total of $25.50 The ice coffees cost a total of $18.50. How much does one ice coffee cost? What is the cost of one frappuccino?

Multiple Choice

What is the first thing that you need to do to solve this problem?

• find the ratios you need and write them down

• add 5 and 3

• $25.50 and $18.50

• divide $25.50 by five

Step 1: Find the ratios and rates

• The first ratio and rate you can see is that there are 8 total items purchased.  5  are ice coffees and 3 are frappuccinos. The total cost is $25.50 So the first ratio would be cost over items. 

   $\frac{Total\ Cost}{items\ bought}$  or  $\frac{25.50}{8}$  

• The second ratio we can see is when only focus on the Ice Coffees. There are 5 ice coffees with a cost of $18.50

• This could be written as  $\frac{total\cos t\ of\ ice\ coffees}{number\ of\ ice\ coffees}$  or  $\frac{18.50}{5}$  

Step 2: Write an equation (proportion)

• They ask you to find the cost of one ice coffee. So set up an equation

•  $\frac{\cos t\ of\ iced\ coffees}{number\ of\ iced\ coffees}$   $=\frac{\cos t}{one\ ice\ coffee}$  

•  $\frac{\text{18.50}}{5}$   $=\frac{\cos t\ \left(x\right)}{1}$  

Multiple Choice

There are five ice coffees that cost $18.50 altogether. How much is one ice coffee?

 $\frac{18.50}{5}=\frac{x}{1}$  

• $3.25

• $5.01

• $3.70

• 4.21

Once you find the cost of each Ice Coffee you can try to find the answer to the second part of the question. "What is the cost of one frappuccino?"

Open Ended

How do you find the cost of the total number of frappuccinos?

To find the cost of the Frappuccinos you have to know how we got the total cost.

•  Ice Coffees $+$  Frappuccinos $=$  Total Cost

• So if we subtract the cost of the Ice Coffees from the Total cost, it will tell us what the total cost of the Frappuccinos is.  

• Total Cost $-$  Cost of ice coffees $=$  Cost of Frappuccinos

Multiple Choice

 $-$  Total Cost

 $-$  Ice Coffees $=$  Frappuccinos

$25.50 $-$  $18.50 $=$  

• $7

• $7.50

Now that we know that the total cost of the Frappuccinos is $7 we can answer the second part of the question. "What is the cost of one frappuccino? "

Multiple Choice

How many frappuccinos were purchased according to the problem?

• 8

• 5

• 3

• 4

Since we have 3 frappuccinos with a cost of $7 we can do Step 1: Create a ratio

 $\frac{total\ \cos t\ of\ Frappuccinos}{number\ of\ frappuccinos\ purchased}$  

Multiple Choice

How should we write the ratio of the cost of the Frappuccinos to the number purchased?

• $\frac{\text{}\text{7}}{3}$

• $\frac{3}{7}$

Step 2: Create the equation

•  $\frac{\text{}7dollars}{3\ frappuccinos}=\frac{\cos t}{1\ frappuccino}$  

Multiple Choice

What is the cost of one frappuccino if three cost $7?

• $7

• $2.33

• $1

• $2.34