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# 7.17: Smart Shopping Extras

Difficulty Level: At Grade Created by: CK-12

Extra for Experts – Smart Shopping - Reason Proportionally Using Least Common Multiples

Solutions

\begin{align*}1. \quad \text{Least common multiple of} \ 4 \ \text{and} \ 5 \ \text{is} \ 20.\!\\ {\;} \quad \ \text{Noble's Books has the better buy.}\!\\ \\ {\;} \quad \ \text{Brown:} \ 4 \ \text{for} \ \19 \ \text{is}\!\\ {\;} \quad \quad \ 20 \ \text{for} \ 5 \times \19, \ \text{or} \ \95\!\\ {\;} \quad \ \text{Noble:} \ 5 \ \text{for} \ \23 \ \text{is}\!\\ {\;} \quad \quad \ 20 \ \text{for} \ 4 \times \23, \ \text{or} \ \92\!\\ {\;} \quad \quad \ \95 > \92\end{align*}

\begin{align*}2. \quad \text{Least common multiple of} \ 2 \ \text{and} \ 4 \ \text{is} \ 4.\!\\ {\;} \quad \ \text{Brown's Books has the better buy.}\!\\ \\ {\;} \quad \ \text{Brown:} \ 2 \ \text{for} \ \25 \ \text{is}\!\\ {\;} \quad \quad \ 4 \ \text{for} \ 2 \times \25, \ \text{or} \ \50\!\\ {\;} \quad \ \text{Noble:} \ 4 \ \text{for} \ \51\!\\ {\;} \quad \quad \ \50 < \51\end{align*}

\begin{align*}3. \quad \text{Least common multiple of} \ 4 \ \text{and} \ 6 \ \text{is} \ 12.\!\\ {\;} \quad \ \text{Noble's Books has the better buy.}\!\\ \\ {\;} \quad \ \text{Brown:} \ 4 \ \text{for} \ \37 \ \text{is}\!\\ {\;} \quad \quad \ 12 \ \text{for} \ 3 \times 37, \ \text{or} \ \111\!\\ {\;} \quad \ \text{Noble:} \ 6 \ \text{for} \ \49 \ \text{is}\!\\ {\;} \quad \quad \ 12 \ \text{for} \ 2 \times \49, \ \text{or} \ \98\!\\ {\;} \quad \quad \ \111 > \98\end{align*}

What is the least common multiple of 4 and 5? Which store has the better buy? How did you figure it out?

What is the least common multiple of 2 and 4? Which store has the better buy? How did you figure it out?

What is the least common multiple of 4 and 6? Which store has the better buy? How did you figure it out?

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Date Created:
Feb 23, 2012
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May 14, 2015
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CK.MAT.ENG.SE.1.Algebra-Explorations-K-7.7.17