Sasha, Julia, and Vika go shopping. Sasha spends $8 less than twice the amount that Vika spent. Julia spends $12 more than Vika spent. The three shoppers spent $204 in all. How much did each girl spend?

Answer 1

Let the amount Vika spends be denoted as \( V \).

According to the problem:

• Sasha spends \( 2V - 8 \) dollars.
• Julia spends \( V + 12 \) dollars.

The total amount spent by the three girls is given as:

\[ V + (2V - 8) + (V + 12) = 204 \]

Now, we can simplify this equation:

\[ V + 2V - 8 + V + 12 = 204 \]

Combining like terms:

\[ 4V + 4 = 204 \]

Next, we can isolate \( V \) by first subtracting 4 from both sides:

\[ 4V = 200 \]

Now, dividing both sides by 4 gives us:

\[ V = 50 \]

Now that we know Vika's spending, we can calculate how much Sasha and Julia spent.

1. Vika's spending: \[ V = 50 \]

2. Sasha's spending: \[ 2V - 8 = 2(50) - 8 = 100 - 8 = 92 \]

3. Julia's spending: \[ V + 12 = 50 + 12 = 62 \]

Finally, we have:

• Vika spends \( 50 \) dollars.
• Sasha spends \( 92 \) dollars.
• Julia spends \( 62 \) dollars.

Now we can verify that the total is correct:

\[ 50 + 92 + 62 = 204 \]

Thus, the amounts spent by each girl are:

• Sasha: $92
• Julia: $62
• Vika: $50