Algebra Weights - 3 Scales, 2 Shapes (Simple Substitution, Simple Answer), to Equation (Level 1) - Mobius Math Academy

Algebra Weights - 3 Scales, 2 Shapes (Simple Substitution, Simple Answer), to Equation

Level 1

This math topic focuses on solving algebraic equations based on visual representations involving scales and different shapes. The problems are designed for advanced basic concepts in algebra, where students must interpret information from images showing balances with variable weights. Each question challenges students to identify the correct set of equations that correspond to the depicted scales, where multiple-choice answers express simple to complex relationships and substitutions. The exercises are intended to improve students’ understanding of forming and solving linear equations, reinforcing algebraic thinking and problem-solving skills.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Algebra Weights - 3 Scales, 2 Shapes (Simple Substitution, Simple Answer), to Equation Worksheet

Algebra Weights - 3 Scales, 2 Shapes (Simple Substitution, Simple Ans...

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}4a+3b &= 11\\2a+2b &= 6\\b &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}5a+b &= 11\\2a+7b &= 6\\3b+a &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}5a+3b &= 11\\2a+4b &= 6\\3b &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}5a+3b &= 11\\2a+4b &= 6\\3b+a &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}3a+3p &= 18\\2a+5p &= 21\\7p &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}3a+2p &= 18\\3a+3p &= 21\\p &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}3a+5p &= 18\\3a+5p &= 21\\5p &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}3a+2p &= 18\\3a+3p &= 21\\2p &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}4b+5p &= 20\\3b+9p &= 22\\p &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}4b+4p &= 20\\2b+6p &= 22\\p &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}4b+5p &= 20\\3b+6p &= 22\\2p &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}6b+5p &= 20\\5b+9p &= 22\\p+b &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}2b &= 23\\3b+4a &= 21\\4a+2b &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}4b+3a &= 23\\3b+3a &= 21\\4a &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}4b &= 23\\3b+4a &= 21\\4a+b &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}4b+3a &= 23\\3b+3a &= 21\\a &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}2p+3a &= 8\\3p+3a &= 9\\a &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}3p+2a &= 8\\2p &= 9\\a &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}2p+2a &= 8\\3p &= 9\\a &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}3p+2a &= 8\\2p &= 9\\2a &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}a+4b &= 28\\5a &= 31\\b+a &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}2a+4b &= 28\\4a+3b &= 31\\b &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}a+4b &= 28\\5a+b &= 31\\b+a &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}a+4b &= 28\\4a &= 31\\b &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}4a+p &= 11\\2a+4p &= 16\\p &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}4a+p &= 11\\2a+4p &= 16\\p+a &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}6a+p &= 11\\4p &= 16\\p+a &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}4a+p &= 11\\2a+4p &= 16\\p+2a &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}4b &= 24\\2b+a &= 18\\2b &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}6b+2a &= 24\\3b+3a &= 18\\a &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}4b+2a &= 24\\3b+a &= 18\\4b &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}6b+2a &= 24\\3b+3a &= 18\\b &= ?\end{align*}$