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Difficulty Level: At Grade Created by: CK-12

Look at the pictures below. Can you figure out which store sells 1 box of noodles for less? In this concept, we will learn how to calculate the unit price of items in order to figure out which store has the better buy.

Guidance

In order to figure out which item is the better buy, like in the question above, we can use the problem solving steps to help.

• Start by describing what you see the pictures.
• Next, figure out what your job is in this problem. In all of these problems your job will be to figure out which item is the better buy.
• Then, make a plan for how you will solve. In these problems, you will want to figure out the unit price of the item at each store. Then, figure out which unit price is less.
• Next, solve the problem.
• Finally, check to make sure that the unit price at the store you chose is lower.

Example A

Look at the picture below. Which store sells a gallon of milk for less? How much would it cost to buy 2 gallons of Milk at Mac's?

Solution:

We can use the problem solving steps to help us with the first question.

\begin{align*}& \mathbf{Describe:} && \text{Mac's and Zac's sell milk.}\\ &&& \text{Mac's: 1 gallon is \4}\\ &&& \text{Zac's: 2 gallons are \10}\\ & \mathbf{My \ Job:} && \text{Figure out the cost of one gallon of milk at Mac's and at Zac's.}\\ &&& \text{Then tell which costs less.}\\ & \mathbf{Plan:} && \text{At Mac's, one gallon is \4.}\\ &&& \text{At Zac's, 2 gallons are \10.}\\ &&& \text{To figure out the cost of one gallon, take half of \10.}\\ &&& \text{Then compare the prices.}\\ & \mathbf{Solve:} && \text{Half of \10 is \5. So, one gallon of milk at Zac's is \5.}\\ &&& \text{One gallon of milk costs less at Mac's than at Zac's.}\\ & \mathbf{Check:} && \text{\4 is less than \5}\end{align*}

The second question was: how much would it cost to buy 2 gallons of Milk at Mac's? Since one gallon of milk at Mac's is $4, two gallons of milk at Mac's is$4+$4=$8.

Example B

Look at the picture below. Which store sells a bottle of water for less? How much would it cost to buy 3 bottles of water at Mac's?

Solution:

We can use the problem solving steps to help us with the first question.

\begin{align*}& \mathbf{Describe:} && \text{Mac's and Zac's sell water.}\\ &&& \text{Mac's: 1 bottle is \2}\\ &&& \text{Zac's: 3 bottles are \3}\\ & \mathbf{My \ Job:} && \text{Figure out the cost of one bottle of water at Mac's and at Zac's.}\\ &&& \text{Then tell which costs less.}\\ & \mathbf{Plan:} && \text{At Mac's, one bottle is \2.}\\ &&& \text{At Zac's, 3 bottles are \3.}\\ &&& \text{To figure out the cost of one bottle, take one third of \3.}\\ &&& \text{Then compare the prices.}\\ & \mathbf{Solve:} && \text{One third of \3 is \1. So, one bottle of water at Zac's is \1.}\\ &&& \text{One bottle of water costs less at Zac's than at Mac's.}\\ & \mathbf{Check:} && \text{\1 is less than \2}\end{align*}

The second question was: how much would it cost to buy 3 bottles of water at Mac's? Since one bottle of water at Mac's is $2, three bottles of water at Mac's is$2+$2 +$2=6. Example C Look at the picture below. Which store sells a pound of onions for less? How much would it cost to buy 2 pounds of onions at Zac's? Solution: We can use the problem solving steps to help us with the first question. \begin{align*}& \mathbf{Describe:} && \text{Mac's and Zac's sell onions.}\\ &&& \text{Mac's: 2 pounds are 40\cancel{\text{c}}}\\ &&& \text{Zac's: 1 pound is 30\cancel{\text{c}}}\\ & \mathbf{My \ Job:} && \text{Figure out the cost of one pound of onions at Mac's and at Zac's.}\\ &&& \text{Then tell which costs less.}\\ & \mathbf{Plan:} && \text{At Zac's, one pound is 30\cancel{\text{c}}}.\\ &&& \text{At Mac's, 2 pounds are 40\cancel{\text{c}}}.\\ &&& \text{To figure out the cost of one pound, take half of 40\cancel{\text{c}}}.\\ &&& \text{Then compare the prices.}\\ & \mathbf{Solve:} && \text{Half of 40\cancel{\text{c}} is 20\cancel{\text{c}}. So, one pound of onions at Mac's is 20\cancel{\text{c}}.}\\ &&& \text{One pound of onions costs less at Mac's than at Zac's.}\\ & \mathbf{Check:} && \text{20\cancel{\text{c}} is less than 30\cancel{\text{c}}}\end{align*} The second question was: how much would it cost to buy 2 pounds of onions at Zac's? Since one pound of onions at Zac's is \begin{align*}30\cancel{\text{c}}\end{align*}, 2 pounds of onions at Zac's is \begin{align*}30\cancel{\text{c}} +30\cancel{\text{c}}=60\cancel{\text{c}}\end{align*}. Concept Problem Revisited \begin{align*}& \mathbf{Describe:} && \text{Mac's and Zac's sell noodles.}\\ &&& \text{Mac's: 1 box is \5}\\ &&& \text{Zac's: 2 boxes are \8}\\ & \mathbf{My \ Job:} && \text{Figure out the cost of one box of noodles at Mac's and at Zac's.}\\ &&& \text{Then tell which costs less.}\\ & \mathbf{Plan:} && \text{At Mac's, one box is \5.}\\ &&& \text{At Zac's, 2 boxes are \8.}\\ &&& \text{To figure out the cost of one box, take half of \8.}\\ &&& \text{Then compare the prices.}\\ & \mathbf{Solve:} && \text{Half of \8 is \4. So, one box of noodles at Zac's is \4.}\\ &&& \text{One box of noodles costs less at Zac's than at Mac's.}\\ & \mathbf{Check:} && \text{\4 is less than \5}\end{align*} Vocabulary A unit price is the cost of one item. In this concept, we are given the overall price for multiple items and need to find the unit price in order to figure out which store has the better buy. Guided Practice Use the picture below for problems 1-3. 1. Which store sells 1 cactus plant or less? 2. How did you decide? 3. How much would it cost to buy 3 cactus plants at Mac’s? Use the picture below for problems 4-6. 4. Which store sells 1 box of strawberries for less? 5. How did you decide? 6. How much would it cost to buy 4 boxes of strawberries at: Mac’s? ________________________________ Zac’s? _________________________________ Answers: 1. Zac’s 2. Mac’s: 1 plant is12. Zac’s: Since 3 plants cost $30, 1 plant is$10. \begin{align*}\10 < \12\end{align*}

3. \begin{align*}\12 + \12 + \12\end{align*}, or $36 4. Mac’s 5. Mac’s: 1 box is half of$6, or $3 Zac’s: 1 sack is half of$8, or 4. \begin{align*}\3 < \4\end{align*} 6. Mac’s:12

Zac’s: \$16

Practice

Use the picture below for problems 1-4.

1. Which store sells 1 sack of oranges for less?
2. How did you decide?
3. How much would it cost to buy 4 sacks of oranges at Mac's?
4. How much would it cost to buy 4 sacks of oranges at Zac's?

Use the picture below for problems 5-8.

1. Which store sells 1 carnation for less?
2. How did you decide?
3. How much would it cost to buy 12 carnations at Mac's?
4. How much would it cost to buy 12 carnations at Zac's?

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Date Created:
Jan 18, 2013