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.