<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

6.3: Boxes and Boxes Extras

Difficulty Level: At Grade Created by: CK-12

Extras for Experts - Boxes and Boxes – Interpret pan balances to determine values of variables

Solutions

\begin{align*}1. \quad t = 2 \ \text{pounds}; \ u = 4 \ \text{pounds}\!\\ {\;} \quad \ \text{From} \ D, 3u = 12, \ \text{so} \ u = 4 \ \text{pounds}.\!\\ {\;} \quad \ \text{From} \ C, 2t = 4, \ \text{so} \ t = 2 \ \text{pounds}.\end{align*}

\begin{align*}2. \quad v = 3 \ \text{pounds}; w = 1 \ \text{pounds}\!\\ {\;} \quad \ \text{From} \ H, v < 5 \ \text{or} \ 1, 2, 3 \ \text{or} \ 4 \ \text{pounds}.\!\\ {\;} \quad \ \text{From} \ G, v = 3w, \ \text{so} \ v \ \text{must be a multiple of} \ 3.\!\\ {\;} \quad \ \text{Then} \ 3 = 3w \ \text{and} \ w \ \text{is} \ 1 \ \text{pound}.\end{align*}

\begin{align*}3. \quad y = 4, 8, \ \text{or} \ 12 \ \text{pounds}; z = 1, 2, \ \text{or} \ 3 \ \text{pounds}\!\\ {\;} \quad \ \text{From} \ J, y < 16 \ \text{or} \ 1, 2, 3, ..., 15 \ \text{pounds}.\!\\ {\;} \quad \ \text{From} \ K, y = 4z, \ \text{so} \ y = \ \text{must be a multiple of} \ 4.\!\\ {\;} \quad \ \text{The possible multiples of} \ 4 \ \text{that are less than} \ 16 \ \text{are} \ 4, 8, \ \text{and} \ 12.\!\\ {\;} \quad \ \text{If} \ y = 4, 8, \ \text{or} \ 12, \ \text{then} \ z = 1, 2, \ \text{or} \ 3 \ \text{pounds}.\end{align*}

\begin{align*}4. \quad r = 1, 2 \ \text{or} \ 3 \ \text{pounds}; s = 10 \ \text{pounds}\!\\ {\;} \quad \ \text{From} \ B, 2s = 20, \ \text{so} \ s = 10 \ \text{pounds}.\!\\ {\;} \quad \ \text{From} \ A, 3r < 10, \ \text{or} \ 1, 2, 3, ..., 9 \ \text{pounds. So} \ r = 1, 2, \ \text{or} \ 3 \ \text{pounds}.\end{align*}

All weights are whole numbers of pounds.

What could be the weights? Tell how you figured it out.

All weights are whole numbers of pounds.

What could be the weights? Tell how you figured it out.

Image Attributions

Show Hide Details
Save or share your relevant files like activites, homework and worksheet.
To add resources, you must be the owner of the section. Click Customize to make your own copy.
Reviews
Help us create better content by rating and reviewing this modality.
Loading reviews...
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
CK.MAT.ENG.SE.1.Algebra-Explorations-K-7.6.3

Original text