Aunt Susan collected $348.80 from the sale of milk shake and bubble tea. She sold 3 times as many cups of milk shake as bubble tea. She collected $131.20 more from the sale of milk shake than the sale of bubble tea. Each cup of bubble tea costs 90¢ more than a cup of milk shake. How many cups of milk shake did Aunt Susan sell?

Let's define the variables:

- Let $ x $ represent the number of cups of bubble tea sold.
- Let $ 3x $ represent the number of cups of milkshake sold (since Aunt Susan sold 3 times as many milkshakes as bubble teas).
- Let $ p $ represent the price of each cup of milkshake (in dollars).
- The price of each cup of bubble tea would then be $ p + 0.90 $ (since each bubble tea costs 90¢ more than a milkshake).

We are given two key pieces of information:

1. Aunt Susan collected $131.20 more from the sale of milkshakes than from the sale of bubble tea. The total amount collected from milkshakes is $ 3x \cdot p $, and from bubble tea is $ x \cdot (p + 0.90) $. Thus, the equation is:
   \[
   3x \cdot p = x \cdot (p + 0.90) + 131.20
   \]
2. The total amount collected from both sales is $348.80. Therefore, the equation for total sales is:
   \[
   3x \cdot p + x \cdot (p + 0.90) = 348.80
   \]

### Step 1: Set up the equations
From equation (1):
\[
3x \cdot p = x \cdot (p + 0.90) + 131.20
\]
Expanding both sides:
\[
3xp = xp + 0.90x + 131.20
\]
Simplifying:
\[
3xp - xp = 0.90x + 131.20
\]
\[
2xp = 0.90x + 131.20
\]
Dividing by $ x $ (assuming $ x \neq 0 $):
\[
2p = 0.90 + \frac{131.20}{x}
\]
\[
2p = 0.90 + \frac{131.20}{x} \tag{3}
\]

From equation (2):
\[
3x \cdot p + x \cdot (p + 0.90) = 348.80
\]
Expanding both sides:
\[
3xp + xp + 0.90x = 348.80
\]
Simplifying:
\[
4xp + 0.90x = 348.80
\]
\[
x(4p + 0.90) = 348.80
\]
\[
4p + 0.90 = \frac{348.80}{x}
\]
\[
4p = \frac{348.80}{x} - 0.90 \tag{4}
\]

### Step 2: Solve the system of equations
Now, solve equations (3) and (4) simultaneously. We can use substitution to find $ x $ and $ p $. Let's proceed with solving.

The solution to the system of equations is:

- The price of each milkshake is $ p = 2.50 $ dollars.
- The number of cups of bubble tea sold is $ x = 32 $.

Since Aunt Susan sold 3 times as many cups of milkshake as bubble tea, the number of milkshakes sold is:
\[
3x = 3 \times 32 = 96
\]

Therefore, Aunt Susan sold 96 cups of milkshake.

Would you like further clarification on any part of the solution? Here are some related questions to deepen your understanding:

1. How would the solution change if each bubble tea cost $1 more than a milkshake?
2. What would happen if Aunt Susan sold 4 times as many milkshakes as bubble tea?
3. How would the total collection change if the price of milkshakes increased by 50¢?
4. If Aunt Susan offered a discount on bubble tea, how would that affect the total sales?
5. What if Aunt Susan sold an equal number of milkshakes and bubble teas—how would that change the problem?

**Tip**: Breaking problems into smaller parts and solving step by step makes complex problems more manageable.

Aunt Susan collected $348.80 from the sale of milkshake and bubble tea. She sold 3 times as many cups of milkshake as bubble tea. She collected $131.20 more from the sale of milkshake than the sale of bubble tea. Each cup of bubble tea costs 90¢ more than a cup of milkshake. How many cups of milkshake did Aunt Susan sell?

Learn how to solve a system of equations to find the number of milkshakes Aunt Susan sold. This algebra problem involves revenue calculations for milkshake and bubble tea sales, suitable for students in Grades 8-10. Explore how to work with linear equations and substitution to solve real-world problems.

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