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Solving equations with bags – NOTES and CLASSWORK

In this lesson you will draw a balance with bags and marbles in order to solve equations.

Example 1

Find the value for n.
3n + 8 = 5n + 2

This equation can be modeled using bags and marbles.

Using the model, we can see that each bag contains 3 marbles. So, n = 3.

We can verify this by substituting 3 for n in the equation.
3n + 8 = 5n + 2
3(3) + 8 = 5(3) + 2
9 + 8 = 15 + 2
17 = 17

Example 2
Sometimes a balance puzzle can be used to solve a problem situation represented by an equation. Even if the problem situation has nothing to do with bags or marbles!

Jenny was filling bottles from a tank of water. When she had filled two bottles with water, 7 liters of water remained in the tank. Then she returned all the water back into the tank. When she had filled four bottles with water 1 liter of water was left in the tank.

Model this problem with bags and marbles. Then solve.

So,

Solving equations with bags - HOMEWORK

Solve the following equations by imagining a balance puzzle. You donÕt have to draw a balance if you donÕt want to. Check each solution by substituting it into the equation.

1. 4s + 5 = 13 + 2s	2. 2a + 3 = a + 10
3. 4y + 6 = 13 + 3y	4. 2h + 9 = 4h + 5
5. 3a + 15 = 7a + 3	6. 4b + 12 = 9b + 2

Represent each of the following situations with an equation. Solve the equation by imagining a balance puzzle. Finally, check your solution by substituting it into the equation.

7. Maya said, ÒI am thinking of a number. If I multiply my number by 6 and add 5, I get the same result as when I multiply it by 3 and add 17.Ó
What is MayaÕs number‌

8. David has three envelopes labeled ÒxÓ and an additional $15. Roxanne has four envelopes labeled ÒxÓ and an additional $9.
How much money must be in each envelope for them to have the same amount of money‌