In this lesson we will begin by solving a puzzle using bags of marbles. Then we will write the algebraic equation represented by the bags and marbles and show that the solution satisfies the equation.

One bag and nine marbles on the left weigh the same as four bags and three marbles on the right. How many marbles are in each bag?

Evaluate the equation for $b = 2$.

Since b = 2 causes both sides of the equation to equal each other, 2 is the correct solution.

Example 1

• Find the number of marbles in each bag.
• Write the equation represented by the model.
• Verify your answer using substitution.

Evaluate the equation for $b = 5$.

$\matrix{b+12&=&3b+2\\5+12&=&(3)(5)+2\\17&=&17\\&\large\surd~&}$

Example 2

• Find the number of marbles in each bag.
• Write the equation represented by the model.
• Verify your answer using substitution.

Evaluate the equation for $b = 5$.

$\matrix{3b+2&=&2b+7\\(3)(5)+2&=&(2)(5)+7\\15+2&=&10+7\\17&=&17\\ &\large\surd~&}$

Question 1

Maria claims that the solution to this puzzle is each bag contains 3 marbles.

Is she correct?

[show answer]

Question 2

Martin says that this puzzle can be represented algebraically as $\)2x+9=4x+1\($ Is he correct?

[show answer]

Question 3

• Find the number of marbles in each bag.
• Write the algebraic equation that this puzzle models.

[show answer]