Solving Equations

6.2.6- Using Equations to Solve Problems



Warm up- Writing equations to fit tape diagrams

Multiple Select

Which equation represents the tape diagram

• 3(a + 2) = 24

• a + 2 = 24

• 3a + 6 = 24

• 24 + 6 = a

Fill in the Blanks

Write an equation to represent the tape diagram?

Multiple Choice

Which equation represents the tape diagram

• x + 39 = 87

• 4x + 87 = 39

• 4x +39 = 87

• x + 87 = 39

Fill in the Blanks

Write an equation to represent the tape diagram?

The employee at the Skee-Ball booth gives you four balls. They explain that your goal is to roll the ball up the ramp into the holes labeled with points. With each ball, you can score the following number of points:

• 1,000 points

• 2,000 points

• 3,000 points

• 4,000 points

• 5,000 points

• 10,000 points
  

You need 15,000 points to win a prize.

After you roll one of your balls, you earn 3,000 points and have three balls left.

How many points do you need to earn on each of your remaining throws to end up with 15,000 points?

Ever play Skee-Ball?

What does each represent in Tyler’s tape diagram?

X represents ______________________

66 represents _____________________

122 represents ____________________

Tyler is making invitations to the fair. He has already made some invitations and wants to finish the rest within a week.

He is trying to spread out the remaining work to make the same number of invitations each day. Tyler draws a diagram to represent the situation.

Match

Match the parts of the equations

• x

• 122

• 66

Amount of remaining invitations per day

Total number of initiations

Invitations already completed

• Amount of remaining invitations per day

• Total number of initiations

• Invitations already completed

Fill in the Blanks

Using Tyler's tape diagram solve for how many invitations he needs to complete each day.

7x + 66 = 122

Noah and his sister are making prize bags for a game at the fair. Noah is putting 7 erasers in each bag and his sister is putting in some number of stickers. After filling 3 of the bags, they have used 57 items.

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Match

Noah and his sister are making prize bags for a game at the fair. Noah is putting 7 erasers in each bag and his sister is putting in some number of stickers. After filling 3 of the bags, they have used 57 items.

Match each piece of information with the corresponding piece from the diagram.

• Total number of items

• Number of stickers

• Number of erasers

• Number of bags being filled

57

x

7

3

• 57

• x

• 7

• 3

Fill in the Blanks

What equations could be written to fit the tape diagram?

Fill in the Blanks

Solve for the number of erasers in each bag

3(x + 7) = 57

Reorder

Order the steps in solving the equation

-6x + 7 = 37

• Subtract 7 from 37

• New equation

  -6x = 30

• Divide -6 to 30

• Solution

  x = -5

1

2

3

4

• 1
• 2
• 3
• 4

Fill in the Blanks

Solve for p

-p - 12 = -2

Reorder

Order the steps in solving the equation

3(x + 13) = 27

• Divide 3 on both sides

• New equation:

  x + 13 = 9

• Subtract 13 from both sides

• Solution:

  x = -4

1

2

3

4

• 1
• 2
• 3
• 4

Draw

Solve for h

5(h + 4) = -10

Review