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6.14: Bargain Shopping

Difficulty Level: At Grade Created by: CK-12

Teacher Notes

In Bargain Shopping signs show prices for the same item at two different stores. At one store, the price is a multiple of the number of units, so the unit price can be easily determined by dividing. At the other store, the price is not a multiple of the number of units. To determine the better buy, students have to equate the number of items from both stores and compare prices.

Solutions

\begin{align*}1. \ \text{Art's Supplies; Art's Supplies:} \ 18 \div 2 = \$9/ \text{brush and} \ 3 \times 9 = \$27 \ \text{for} \ 3 \ \text{brushes.}\!\\ {\;} \quad \$27 < \$28.\end{align*}

\begin{align*}2. \ \text{Art's Supplies; Art's Supplies:} \ 35 \div 5 = \$7/\text{jar and} \ 6 \times 7 = \$42 \ \text{for} \ 6 \ \text{jars.}\!\\ {\;} \quad \$42 < \$43.\end{align*}

\begin{align*}3. \ \text{Picture It; Art's Supplies:} \ 15 \div 3 = \$5/\text{palette and} \ 4 \times 5 = \$20 \ \text{for} \ 4 \ \text{palettes.}\!\\ {\;} \quad \$19 < \$20.\end{align*}

\begin{align*}4. \ \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*}5. \ \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*}6. \ \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*}

Bargain Shopping - Reason Proportionally

Which store has the better buy for 3 boxes of pastels?

\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*}

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

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

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

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

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

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

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

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CK.MAT.ENG.SE.1.Algebra-Explorations-K-7.6.14