TWO-STEP EQUATIONS
Math 8
Let’s return to the story of King Midas and his children, Prince Charming and Princess Perfect. The king has more gifts to give and he will leave them on two tables in the royal treasury. He is giving his children the same amount of coins each week.
In each of the following situations determine how many coins are in each bag. Draw a picture to represent each situation. Illustrate how you found the number of coins in each bag using the picture.
Week 1:
Princess Perfect received 2 bags and four gold coins on her table while
Prince Charming received 12 coins. How many coins are in each bag?
Princess
Prince
=
Set aside 4 loose coins from each child.
Split the remaining items into equal groups
Each bag contains 4 coins
Week 2: The king has saved a bunch of coins for the twins. The Prince
has 3 bags and 7 coins. The Princess has 16 coins. How many coins are
in each bag if the king loves them both equally?
Princess
Prince
=
Set aside 7 loose coins from each child.
Split the remaining items into equal groups
Each bag contains 3 coins
Week 3: Today in the treasury, the Prince found 4 bags and 6 coins. The Princess found 10 coins. How many coins are in each bag?
Princess
Prince
Set aside 6 loose coins
from each child.
Split the remaining items into equal groups
Each bag contains just a single coin
=
Week 4: If the Prince received 22 coins and the Princess got 2 bags and 7 loose gold coins, how many coins are in each bag?
Prince
Princess
=
Set aside 7 loose coins
from each child.
Split the remaining items into equal groups
Each bag contains 7 whole coins and a half coin
Do the 15 remaining
coins split evenly?
Steps for solving 2-Step Problems
1. Locate the variable, and determine which number is most closely connected to it,
save this number for later (it is the “best friend” of the variable)
-often it is closest by multiplication/division, unless grouping symbols are involved
2. Use inverse operations to move the other number away (send home the “regular friend” of the variable)
3. Use inverse operations to isolate the variable (send home the “best friend” of the variable)
4. Check your solution!!
Solve each problem.
You can either divide both sides�by the fraction coefficient, OR
multiply both sides by the reciprocal
Solve each problem.
Solve each problem.
Check your solution!!
Common Error!!
Correct Solution!!
Solve each problem.
Solve each problem.
( )
Hidden Parentheses show strongest connection
Solve each problem.
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Solve each problem.