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8.7: Hanging Scales Extra for Experts

Difficulty Level: At Grade Created by: CK-12
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Extra for Experts Hanging Scales – Solve for Unknowns

Solutions

\begin{align*}1. \ A: x + z + z = 19; \ B: x + y + z + z = 28; \ C: w + x + z + z = 25; \ D: w + y + w + y = 10\!\\ {\;} \quad w = 6 \ pounds, \ x = 5 \ pounds, \ y = 9 \ pounds, \ z = 7 \ pounds\!\\ 2. \ A: w + x + y = 19; \ B: w + x + z = 22; \ C: w + x + y + y = 26; \ D: w + z + w + z = 36:\!\\ {\;} \quad w = 8 \ pounds, \ x = 4 \ pounds, \ y = 7 \ pounds, \ z = 10 \ pounds\!\\ 3. \ A: x + y + y = 29; \ B: x + x + y + y = 36; \ C: w + x + y + y = 38; \ D: w + z + z = 25:\!\\ {\;} \quad w = 9 \ pounds, \ x = 7 \ pounds, \ y = 11 \ pounds, \ z = 8 \ pounds\end{align*}

Write equations. Figure out the weights of the blocks. Same blocks weigh the same.

1.

\begin{align*}w = ? \ pounds, x = \underline{?} \ pounds, y = \underline{?} \ pounds, z = \underline{?} \ pounds\end{align*}

2.

\begin{align*}w = ? \ pounds, x = \underline{?} \ pounds, y = \underline{?} \ pounds, z = \underline{?} \ pounds\end{align*}

3.

\begin{align*}w = ? \ pounds, x = \underline{?} \ pounds, y = \underline{?} \ pounds, z = \underline{?} \ pounds\end{align*}

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CK.MAT.ENG.SE.1.Algebra-Explorations-K-7.9.7