# 6.6: Bargain Shopping

Difficulty Level: At Grade Created by: CK-12

Look at the signs below for the price of pastels at two different stores. Which store has the better buy for 3 boxes of pastels? In this concept, we will practice comparing the prices of items in order to determine 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 one of the stores. Then, compare the price for the number of items in the problem.
• Next, solve the problem.
• Finally, check to make sure that the price at the store you chose is lower.

#### Example A

Which store has the better buy for 3 brushes? How did you decide?

Solution:

We can use problem solving steps to help.

\begin{align*}& \mathbf{Describe:} && \text{Two stores sell brushes.}\!\\ &&& \text{Art's Supplies:} \ 2 \ \text{brushes for} \ \18\!\\ &&& \text{Picture It:} \ 3 \ \text{brushes for} \ \28\!\\ & \mathbf{My \ Job:} && \text{Decide which store has the better buy.}\!\\ & \mathbf{Plan:} && \text{I'll start with Art's Supplies.}\!\\ &&& \text{I can easily figure out the price of one brush at that store.}\!\\ &&& \text{Then I'll find the cost of} \ 3 \ \text{brushes at Art's Supplies and compare with Picture It.}\!\\ & \mathbf{Solve:} && \text{Art's Supplies:} \ 2 \ \text{brushes for} \ \18 \ \text{is} \ 18 \div 2, \ \text{or} \ \9 \ \text{per brush.}\!\\ &&& \qquad \qquad \quad 3 \ \text{brushes at Art's Supplies are} \ 3 \times 9, \ \text{or} \ \27.\!\\ &&& \qquad \qquad \quad \27 \ \text{is less than} \ \28. \ \text{So Art's Supplies has the better buy.}\!\\ & \mathbf{Check:} && \text{Art's Supplies:} \ \18 \div 2= 9 \ \text{and} \ 3 \times 9 = \27.\!\\ &&& \qquad \qquad \quad \27 < \28\end{align*}

#### Example B

Which store has the better buy for 6 jars of oil paints? How did you decide?

Solution:

We can use problem solving steps to help.

\begin{align*}& \mathbf{Describe:} && \text{Two stores sell jars of oil paints.}\!\\ &&& \text{Art's Supplies:} \ 5 \ \text{jars for} \ \35\!\\ &&& \text{Picture It:} \ 6 \ \text{jars for} \ \43\!\\ & \mathbf{My \ Job:} && \text{Decide which store has the better buy.}\!\\ & \mathbf{Plan:} && \text{I'll start with Art's Supplies.}\!\\ &&& \text{I can easily figure out the price of one jar at that store.}\!\\ &&& \text{Then I'll find the cost of} \ 6 \ \text{jars at Art's Supplies and compare with Picture It.}\!\\ & \mathbf{Solve:} && \text{Art's Supplies:} \ 5 \ \text{jars for} \ \35 \ \text{is} \ 35 \div 5, \ \text{or} \ \7 \ \text{per jar.}\!\\ &&& \qquad \qquad \quad 6 \ \text{jars at Art's Supplies are} \ 6 \times 7, \ \text{or} \ \42.\!\\ &&& \qquad \qquad \quad \42 \ \text{is less than} \ \43. \ \text{So Art's Supplies has the better buy.}\!\\ & \mathbf{Check:} && \text{Art's Supplies:} \ \35 \div 5 = 7 \ \text{and} \ 6 \times 7 = \42.\!\\ &&& \qquad \qquad \quad \42 < \43\end{align*}

#### Example C

Which store has the better buy for 4 palettes? How did you decide?

Solution:

We can use problem solving steps to help.

\begin{align*}& \mathbf{Describe:} && \text{Two stores sell palettes.}\!\\ &&& \text{Art's Supplies:} \ 3 \ \text{palettes for} \ \15\!\\ &&& \text{Picture It:} \ 4 \ \text{palettes for} \ \19\!\\ & \mathbf{My \ Job:} && \text{Decide which store has the better buy.}\!\\ & \mathbf{Plan:} && \text{I'll start with Art's Supplies.}\!\\ &&& \text{I can easily figure out the price of one palette at that store.}\!\\ &&& \text{Then I'll find the cost of} \ 4 \ \text{palettes at Art's Supplies and compare with Picture It.}\!\\ & \mathbf{Solve:} && \text{Art's Supplies:} \ 3 \ \text{palettes for} \ \15 \ \text{is} \ 15 \div 3, \ \text{or} \ \5 \ \text{per palette.}\!\\ &&& \qquad \qquad \quad 4 \ \text{palettes at Art's Supplies are} \ 4 \times 5, \ \text{or} \ \20.\!\\ &&& \qquad \qquad \quad \19 \ \text{is less than} \ \20. \ \text{So Picture It has the better buy.}\!\\ & \mathbf{Check:} && \text{Art's Supplies:} \ \15 \div 3 = 5 \ \text{and} \ 4 \times 5 = \20.\!\\ &&& \qquad \qquad \quad \19 < \20\end{align*}

#### Concept Problem Revisited

We can use problem solving steps to help.

\begin{align*}& \mathbf{Describe:} && \text{Two stores sell boxes of pastels.}\!\\ &&& \text{Art's Supplies:} \ 3 \ \text{boxes for} \ \25\!\\ &&& \text{Picture It:} \ 4 \ \text{boxes for} \ \28\!\\ & \mathbf{My \ Job:} && \text{Decide which store has the better buy.}\!\\ & \mathbf{Plan:} && \text{I'll start with Picture It.}\!\\ &&& \text{I can easily figure out the price of one box of pastels at that store.}\!\\ &&& \text{Then I'll find the cost of} \ 3 \ \text{boxes of pastels at Picture It and compare with Art's Supplies.}\!\\ & \mathbf{Solve:} && \text{Picture It:} \ 4 \ \text{boxes for} \ \28 \ \text{is} \ 28 \div 4, \ \text{or} \ \7 \ \text{per box.}\!\\ &&& \qquad \qquad \quad 3 \ \text{boxes at Picture It are} \ 3 \times 7, \ \text{or} \ \21.\!\\ &&& \qquad \qquad \quad \21 \ \text{is less than} \ \25. \ \text{So Picture It has the better buy.}\!\\ & \mathbf{Check:} && \text{Picture It:} \ \28 \div 4 = 7 \ \text{and} \ 3 \times 7 = \21.\!\\ &&& \qquad \qquad \quad \21 < \25\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 first find the unit price in order to help us to figure out which store has the better buy.

### Guided Practice

1. Which store has the better buy for 7 palette knives? How did you decide?

2. Which store has the better buy for 4 pads of drawing paper? How did you decide?

3. Which store has the better buy for 2 canvases? How did you decide?

\begin{align*}1. \ \text{Picture It; Art's Supplies:} \ 40 \div 5 = \8/\text{knife and} \ 7 \times 8 = \56 \ \text{for} \ 7 \ \text{knives.}\!\\ {\;} \quad \54 < \56.\end{align*}

\begin{align*}2. \ \text{Art's Supplies; Picture It:} \ 60 \div 6 = \10/\text{pad and} \ 4 \times 10 = \40 \ \text{for} \ 4 \ \text{pads.}\!\\ {\;} \quad \37 < \40.\end{align*}

\begin{align*}3. \ \text{Picture It; Picture It:} \ 27 \div 3 = \9/\text{canvas and} \ 2 \times 9 = \18 \ \text{for} \ 2 \ \text{canvases.}\!\\ {\;} \quad \18 < \23.\end{align*}

### Practice

Use the facts on the signs. Figure out the better buy.

1. Which store has the better buy for 3 carnations? How did you decide?

2. Which store has the better buy for 3 mum plants? How did you decide?

3. Which store has the better buy for 9 bud vases? How did you decide?

4. Which store has the better buy for 6 pounds of potting soil? How did you decide?

5. Which store has the better buy on 7 bamboo shoots? How did you decide?

6. Which store has the better buy for 6 roses? How did you decide?

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Date Created:
Jan 18, 2013