Janice and Siti had some money in the rallo 2: 3. After each of them spent $32 on a school bag, Janice had 3 das much money as Siti. How much money did Siti have in the end?

Let's solve the problem step by step.

### Step 1: Define Variables
Let the initial amounts of money that Janice and Siti had be $ J $ and $ S $ respectively. According to the problem, the ratio of their money was $ J : S = 2 : 3 $.

So, we can express this as:
\[
J = 2x \quad \text{and} \quad S = 3x
\]
where $ x $ is a common multiplier.

### Step 2: Account for the Money Spent
Each of them spent $32 on a school bag. So, the amount of money they have left is:
\[
\text{Janice's remaining money} = 2x - 32
\]
\[
\text{Siti's remaining money} = 3x - 32
\]

### Step 3: Set Up the Equation
According to the problem, after spending the money, Janice had 3 times as much money as Siti:
\[
2x - 32 = 3 \times (3x - 32)
\]

### Step 4: Solve the Equation
Let's solve the equation:
\[
2x - 32 = 9x - 96
\]
Bring all terms involving $ x $ to one side and constant terms to the other:
\[
2x - 9x = -96 + 32
\]
\[
-7x = -64
\]
\[
x = \frac{-64}{-7} = \frac{64}{7} \approx 9.14
\]

### Step 5: Find Siti's Final Amount
We can now find Siti's initial amount:
\[
S = 3x = 3 \times \frac{64}{7} = \frac{192}{7} \approx 27.43
\]

After spending $32, Siti's remaining money is:
\[
\text{Siti's remaining money} = 3x - 32 = \frac{192}{7} - 32
\]
Let's convert $32 to sevenths to subtract:
\[
32 = \frac{224}{7}
\]
Thus:
\[
\text{Siti's remaining money} = \frac{192}{7} - \frac{224}{7} = \frac{-32}{7} = -4.57
\]

It appears that the problem has some inconsistencies as the remaining amount for Siti becomes negative, which is impossible. This implies either a mistake in the interpretation or that the problem has no solution with the given conditions.

Would you like to review any specific part or would you like to ask another question?

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**Related questions:**
1. What would happen if both spent a different amount?
2. How would the problem change if the ratio was different?
3. Can you find out how much Janice had at the end?
4. What if Siti spent more than $32?
5. How do ratios work in problems like this?

**Tip:** Always double-check the conditions given in word problems to ensure they make logical sense.

Explore the solution to the Janice and Siti money problem involving ratios and spending. Learn step-by-step how to solve this mathematical problem. Suitable for Grades 6-8 students.

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