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

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

Level 1

This math topic involves solving algebraic equations based on balances with different weights, represented by visual puzzles. Students engage with algebraic expressions where they determine the values of variables from diagrams of scales balancing different shapes. The skills practiced include complex substitution to simplify equations, forming and solving equations based on visual cues, and making compound answers. It is an advanced exercise in basic algebra concepts, enhancing problem-solving skills through visualization and algebraic manipulation. Each question offers multiple equations and asks which represents the balance shown, promoting critical thinking in equation formulation.

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 (Complex Substitution, Compound Answer), to Equation Worksheet

Algebra Weights - 3 Scales, 2 Shapes (Complex Substitution, Compound ...

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}4b+4a &= 12\\4b+2a &= 8\\b+a &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}4b+4a &= 12\\6b+2a &= 8\\a &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}4b+4a &= 12\\6b+2a &= 8\\3a &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}4b+4a &= 12\\6b+2a &= 8\\2b+a &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}b+4a &= 15\\2b+3a &= 15\\b+a &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}b+4a &= 15\\2b+3a &= 15\\2b+3a &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}b+4a &= 15\\2b+3a &= 15\\2b+a &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}4b+4a &= 15\\b+3a &= 15\\b+3a &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}5p+2b &= 18\\p+4b &= 15\\p+b &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}4p+2b &= 18\\p+5b &= 15\\b &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}4p+2b &= 18\\p+5b &= 15\\p &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}4p+2b &= 18\\p+4b &= 15\\p+b &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

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

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

c $A LaTex expression showing \begin{align*}2b+a &= 4\\b+4a &= 9\\b+a &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}a &= 4\\4a &= 9\\b+a &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}5p+4b &= 20\\2p+4b &= 14\\2p+b &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}7p+4b &= 20\\2p+4b &= 14\\2p+3b &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}7p+4b &= 20\\2p+4b &= 14\\2p+2b &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}4p+4b &= 20\\2p+4b &= 14\\p+b &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}6p &= 16\\5a+3p &= 20\\3p+a &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}2a+4p &= 16\\3a+4p &= 20\\a+p &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}2a+6p &= 16\\3a+3p &= 20\\3p &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}2a+6p &= 16\\3a+3p &= 20\\p &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

a $A LaTex expression showing \begin{align*}3p+5a &= 31\\2a &= 13\\p &= ?\end{align*}$

b $A LaTex expression showing \begin{align*}5p+5a &= 31\\p &= 13\\a &= ?\end{align*}$

c $A LaTex expression showing \begin{align*}3p+4a &= 31\\p+2a &= 13\\p+a &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}3p+4a &= 31\\p+2a &= 13\\a &= ?\end{align*}$

Which equations represent what these scales are showing

An svg image showing a math problem

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

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

c $A LaTex expression showing \begin{align*}7b &= 24\\5a &= 18\\2b &= ?\end{align*}$

d $A LaTex expression showing \begin{align*}4b &= 24\\5a+2b &= 18\\a+2b &= ?\end{align*}$