# Comparison Shopping: Unit Price and Related Measurements07:07 minutes

## Comparison Shopping: Unit Price and Related Measurements Übung

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• #### Find the rate and unit rate from multiple representations.

##### Tipps

To find a unit rate from a table or graph, set up the ratio for the unit rate using information given in either the table or graph.

To find a unit rate from an equation, use opposite operations to bring both variables to one side. For example in $y=\frac{2}{5}x$, bring the $x$ to the left side by dividing both sides by $x$ to get $\frac{y}{x}=\frac{2}{5}$.

The unit rate is the ratio of two measurements in which the second term is $1$.

##### Lösung
• To find the unit rate from a table, pick any row except for the one that contains $(0,0)$. ($(0,0)$ is the origin, which is a part of every proportional relationship, so it will not help us find the unit rate for any specific relationship.) Put the values in the ratio $\frac{\text{Distance}}{\text{Time}}$. Simplify the fraction to get a unit rate.
• To find the unit rate from a graph, first check to see if the graph goes through the origin. This graph does, so the graph represents a direct proportion. To start, pick any point on the line, other than $(0,0)$. Then put the values into the ratio $\frac{\text{Distance}}{\text{Time}}$. Simplify the fraction to get the unit rate.
• To find the unit rate from an equation, isolate the ratio by dividing both sides by $t$. This gives us the proportion $\frac{d}{t}=$unit rate. Simplify the fraction to get a unit rate.
• #### Define rate and unit rate.

##### Tipps

Some examples of rates are: $7$ apples to $6$ oranges, $4$ cups of flour per $2$ cups of milk, and $70$ miles per $2$ hours.

Some examples of unit rates are: defense per point, cost per unit, and miles per hour. Point, unit, and hour are singular.

When simplifying a unit rate, the goal is to make the denominator $1$.

##### Lösung

The definition of unit rate is the ratio of two measurements in which the second term is $1$.

The definition of rate is a ratio that compares two different quantities.

Unit rate and rate are similar because they both compare two measurements, but in a unit rate the second measurement is always reduced to $1$.

• #### Determine the best price by identifying the unit price.

##### Tipps

Determine the unit price for each deal.

Set up the ratio of $\frac{\text{cost}}{\text{unit}}$, then divide to simplify.

For example, let's say a five pack of figurines sold for $\$63.75$. The$\frac{\text{cost}}{\text{unit}}$ratio would be$\frac{63.75}{5}$. Simplified$\frac{63.75}{5}=12.75$. So the unit price for this example is$\$12.75$.

##### Lösung

The order from least to most expensive is:

$1)$ A four pack of Cat Hero figurines for $\$41.50$. • First, set up the$\frac{\text{cost}}{\text{unit}}$ratio:$\frac{41.50}{4}$. • Then, divide$\frac{41.50}{4}=10.35$. • So, the unit price for this deal is$\$10.35$.
$2)$ A single Cat Hero figurine for $\$11.50$. • First, set up the$\frac{\text{cost}}{\text{unit}}$ratio:$\frac{11.50}{1}$. • Then, divide$\frac{11.50}{1}=11.50$. • So, the unit price for this deal is$\$11.50$.
$3)$ A two pack of Cat Hero figurines for $\$24.00$. • First, set up the$\frac{\text{cost}}{\text{unit}}$ratio:$\frac{24.00}{2}$. • Then, divide$\frac{24.00}{2}=12.00$. • So, the unit price for this deal is$\$12.00$.
$4)$ A three pack of Cat Hero figurines for $\$36.75$. • First, set up the$\frac{\text{cost}}{\text{unit}}$ratio:$\frac{36.75}{3}$. • Then, divide$\frac{36.75}{3}=12.25$. • So, the unit price for this deal is$\$12.25$.

• #### Determine the best deal using unit rate.

##### Tipps

Set up the $\frac{\text{cost}}{\text{unit}}$ ratio and simplify.

Make a list of the possible combinations of packs Gabe's sister can buy that will give her a total of five figures. For example $2+3=5$, what are some other combinations? Think outside of the box, she doesn't only have to buy two packs.

Substitute in the cost for each for each pack to determine which combination is the cheapest. For example a two-pack and a three-pack will give her five figurines. The cost of a two-pack is $\$9.50$and the cost of a three pack is$\$13.50$, so the total cost would be $\$23.00$. ##### Lösung To answer this problem, first find the cost per unit for each pack of figurines. • One figurine for$\$5.00$, so $\frac{5.00}{1}=5.00$.
• Two figurines for $\$9.50$, so$\frac{9.50}{2}=4.75$• Three figurines for$\$13.50$, so $\frac{13.50}{3}=4.50$
• Four figurines for $\$17.00$, so$\frac{17.00}{4}=4.25~$The cheapest cost per unit is$\$4.25$ from the four-pack.

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Second, think of all possible combinations of packs that will result in five figurines.

• $2+3=5$
• $1+4=5$
• $2+2+1=5$
• $3+1+1=5$
• $2+1+1+1=5$
• $1+1+1+1+1=5$
$~$

Now, substitute in each cost per pack to determine the cheapest option for five figurines.

• $2+3=5\\ 9.50+13.50=23.00$
• $1+4=5\\5.00+17.00=22.00$
• $2+2+1=5\\ 9.50+9.50+5=24.00$
• $3+1+1=5\\ 13.50+5+5=23.50$
• $2+1+1+1=5\\ 9.50+5.00+5.00+5.00=24.50$
• $1+1+1+1+1=5\\ 5.00+5.00+5.00+5.00+5.00=25.00$
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