Let's denote the number they both start with as $ x $.

1. Malin's operations:
- Subtracts 3 from $ x $: $ x - 3 $
- Divides the result by 5: $ \frac{x - 3}{5} $

2. Shawn's operations:
- Adds 7 to $ x $: $ x + 7 $
- Divides the result by 2: $ \frac{x + 7}{2} $

According to the problem, Malin's final answer is the same as Shawn's final answer. Therefore, we set up the equation:

$$ \frac{x - 3}{5} = \frac{x + 7}{2} $$

To solve for $ x $, we first eliminate the fractions by cross-multiplying:

$$ 2(x - 3) = 5(x + 7) $$

Expanding both sides:

$$ 2x - 6 = 5x + 35 $$

Next, we isolate $ x $ by moving all terms involving $ x $ to one side and constant terms to the other side:

$$ 2x - 5x = 35 + 6 $$

Simplifying:

$$ -3x = 41 $$

Finally, we solve for $ x $:

$$ x = -\frac{41}{3} $$

So, the number they both started with is $ -\frac{41}{3} $.

Question

Let's denote the number they both start with as $ x $.

1. Malin's operations:
   - Subtracts 3 from $ x $: $ x - 3 $
   - Divides the result by 5: $ \frac{x - 3}{5} $

2. Shawn's operations:
   - Adds 7 to $ x $: $ x + 7 $
   - Divides the result by 2: $ \frac{x + 7}{2} $

According to the problem, Malin's final answer is the same as Shawn's final answer. Therefore, we set up the equation:

$$ \frac{x - 3}{5} = \frac{x + 7}{2} $$

To solve for $ x $, we first eliminate the fractions by cross-multiplying:

$$ 2(x - 3) = 5(x + 7) $$

Expanding both sides:

$$ 2x - 6 = 5x + 35 $$

Next, we isolate $ x $ by moving all terms involving $ x $ to one side and constant terms to the other side:

$$ 2x - 5x = 35 + 6 $$

Simplifying:

$$ -3x = 41 $$

Finally, we solve for $ x $:

$$ x = -\frac{41}{3} $$

So, the number they both started with is $ -\frac{41}{3} $.

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