Wei has $150.00 to make a garland using 60-cent balloons. He wants to purchase 100 blue balloons and some number of white balloons. He learns that the white balloons are on sale for half price. He writes and solves an equation to find the number of white balloons he can purchase.

Which models can be used to solve the problem?

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To solve the problem, Wei needs to model the total cost of purchasing 100 blue balloons and some number of white balloons, given that the white balloons are on sale for half price. Here are the steps and models that can be used to solve the problem:

1. **Cost of blue balloons:**
   - The cost for 100 blue balloons at $0.60 each:  
   \[ \text{Cost of blue balloons} = 100 \times 0.60 \]

2. **Cost of white balloons:**
   - Let $ x $ represent the number of white balloons Wei wants to purchase.
   - Since the white balloons are on sale for half price, the cost of each white balloon is $0.30 (half of $0.60).
   - The total cost for $ x $ white balloons:  
   \[ \text{Cost of white balloons} = 0.30 \times x \]

3. **Total cost equation:**
   - The total cost for all the balloons (blue and white) must equal the $150 Wei has:
   \[ 100 \times 0.60 + 0.30 \times x = 150.00 \]

4. **Simplifying the equation:**
   - Simplify and solve for $ x $ (the number of white balloons):
   \[ 60 + 0.30x = 150 \]
   \[ 0.30x = 90 \]
   \[ x = \frac{90}{0.30} \]
   \[ x = 300 \]

So, Wei can purchase 300 white balloons along with the 100 blue balloons.

**Models used to solve the problem:**

1. **Arithmetic Model:** Basic arithmetic operations were used to calculate the cost of the blue balloons and the discounted cost of the white balloons.

2. **Algebraic Model:** An algebraic equation was set up to express the relationship between the total cost and the number of white balloons.

3. **Linear Equation Model:** The problem was modeled using a linear equation in one variable, which was then solved for the unknown number of white balloons.

4. **Substitution Model:** Substituting the known values (cost of blue balloons and total money available) into the equation to isolate the variable $ x $.

5. **Solution Model:** Finally, solving the simplified linear equation gave the answer for the number of white balloons.

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Do you want any details or have any questions? 

Here are some related questions to consider:

1. What would happen if Wei only had $100.00 instead of $150.00?
2. How many blue balloons could Wei buy if the white balloons cost $0.40 each?
3. What if the sale on white balloons was 25% off instead of 50% off?
4. How would the equation change if Wei wanted to buy twice as many white balloons as blue balloons?
5. What would be the cost if Wei decided to buy an equal number of blue and white balloons?

**Tip:** When dealing with discounts, always check the new price per item before setting up your equation.

Learn how to solve Wei's balloon garland problem where he needs to calculate the number of white balloons he can buy with a budget of $150.00. Understand the arithmetic and algebraic models used, including how to set up and solve linear equations. Suitable for students in Grades 6-8.

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