Problem Analysis:
The image presents a mathematical puzzle involving different types of cups, each representing a numerical value. The goal is to determine the value of each type of cup and then solve the given equation.
#### Step 1: Identify the Cups
There are three types of cups in the image:
1. A
small cup (without a sleeve).
2. A
medium cup (with a brown sleeve).
3. A
large cup (with a straw and whipped cream).
#### Step 2: Interpret the First Equation
The first equation is:
\[
\text{Small cup} \times \text{Medium cup} \times \text{Large cup} = 36
\]
Let's denote:
- Small cup = \( S \)
- Medium cup = \( M \)
- Large cup = \( L \)
So, the equation becomes:
\[
S \times M \times L = 36
\]
#### Step 3: Solve for the Values
We need to find integer values for \( S \), \( M \), and \( L \) such that their product is 36. Let's consider possible factorizations of 36:
\[
36 = 1 \times 6 \times 6 \quad \text{(not distinct values)}
\]
\[
36 = 2 \times 3 \times 6 \quad \text{(distinct values)}
\]
\[
36 = 3 \times 3 \times 4 \quad \text{(not distinct values)}
\]
From the options, the most logical distinct values are:
\[
S = 2, \quad M = 3, \quad L = 6
\]
#### Step 4: Verify the Values
Substitute \( S = 2 \), \( M = 3 \), and \( L = 6 \) into the first equation:
\[
S \times M \times L = 2 \times 3 \times 6 = 36
\]
This is correct, so the values are verified.
#### Step 5: Solve the Second Equation
The second equation is:
\[
(\text{Medium cup} \times \text{Medium cup} - \text{Small cup}) \times \text{Large cup} = ?
\]
Substitute the values \( S = 2 \), \( M = 3 \), and \( L = 6 \):
\[
(M \times M - S) \times L = (3 \times 3 - 2) \times 6
\]
#### Step 6: Perform the Calculations
1. Calculate \( M \times M \):
\[
M \times M = 3 \times 3 = 9
\]
2. Subtract \( S \):
\[
9 - 2 = 7
\]
3. Multiply by \( L \):
\[
7 \times 6 = 42
\]
Final Answer:
\[
\boxed{42}
\]
Parent Tip: Review the logic above to help your child master the concept of math puzzles brain teasers.
