Solving One-Step Equations with King Midas and his children�
Solving One-Step Equations
In a fairy tale kingdom lived King Midas who knew how to invest his money wisely and so he saw his wealth increase steadily and became very rich. He wanted to share some of his wealth with his twin children which he loved, Prince Charming and Princess Perfect, but he always wanted to be fair and give them the same amount of gold coins. He placed his gifts of gold coins on two tables in the royal treasury of the palace each week. Sometimes there were bags of coins and other times the coins were just left lying on the table. The bags of coins in the King’s gifts would always hold the same amount of coins as other bags that same week, but the number of coins in a bag could change from week to 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: The Princess has one bag and 6 coins on her table, while the Prince has 19 coins on his table. How many coins are in the bag?
Princess
Prince
The bag must have 13 coins inside
Week 2: Prince Charming has two bags of coins and Princess Perfect has 24 loose coins. How many coins are in each bag?
Princess Prince
Each bag must have 12 coins inside
Week 3: The Princess has 8 gold coins and the Prince has a bag and two gold coins. How many coins are in the bag?
Princess
Prince
=
=
This week the bag contains 6 coins
Week 4: Princess Perfect has four bags of coins lying on her table, and there are 20 coins lying on Prince Charming’s. How many coins are in each bag?
Prince
Princess
=
5 coins in each bag
Next are some images of bags and coins for the next few weeks that the King gave as gifts to his children.
For each of the pictures solve the problem, explain the strategy you used in words, and use symbolic representations to illustrate your strategy
Week 5
=
Explain:
Symbols:
Separate the loose coins into 3 groups, equal
to the number of bags.
1 bag = 4 coins
Week 6
=
Explain:
Symbols:
Match 4 of the loose coins from each table,
the remaining amount is equal to the bag.
1 bag = 8 coins
Week 7
=
Explain:
Symbols:
Separate the loose coins into 6 groups, equal
to the number of bags.
1 bag = 3 coins
Week 8
=
Explain:
Symbols:
Set aside 6 of the loose coins from each table,
the remaining amount is equal to the bag.
1 bag = 30 coins
Because King Midas wanted to keep his gifts the same between his children, we can create equations to solve for how many coins are in the bag. The unknown quantity can change each week, and so we let it be represented by a variable.
When solving a problem, ask yourself what operation (add, subtract, multiply, divide) is happening, and what would be the operation that is the opposite (inverse)?
What if the King didn’t love his children equally? What if he happened to give the Princess more coins than the Prince? If this was the case and the Princess found a bag and 2 coins on her table in the treasury, but the Prince had 5 coins, how many coins could be in the bag?
Princess
Prince
>
How can we illustrate when there are many possibilities of amounts of coins?
1 2 3 4 5
Each bag must have more than 3 coins
Solve each equation or inequality. Graph solutions on a number line
8 9 10 11 12
21 22 23 24 25
Solve.
Solve.
You can check your solutions!
Solve. Graph the solution on a number line
−39
−40
−41
−38 −37
Anytime you
multiply or divide both sides by a negative number
the inequality symbol turns around!