Once you have $0.85P$ equal to $408$, solve for $P$ by dividing by $0.85$. This gives you the price after the first discount but before the second one.

Compare the intermediate price $P$ to the original price $600$. How many dollars were taken off in the first discount, and what fraction of $600$ is that?

After you find the fraction of $600$ that was discounted, convert that fraction to a percentage by multiplying by 100.

In one expression line, type y = 600*(1 - x/100)*0.85. This represents the final price after an $x\\%$ discount followed by a 15% discount.

In a new line, type y = 408. This is the horizontal line representing the actual final price of the laptop.

Look at the point where the curve y = 600*(1 - x/100)*0.85 intersects the line y = 408. The x-coordinate of this intersection gives the value of $x$ that makes the final price $408$.

Let the price after the first discount be $P$ dollars. Then a 15% discount means the customer pays 85% of $P$, or $0.85P$.

We are told this final price is $408$, so:

$0.85P = 408$.

To find $P$, divide both sides of $0.85P = 408$ by $0.85$:

$P = \dfrac{408}{0.85}$.

Compute $408 \div 0.85$:

• Multiply top and bottom by 100: $\dfrac{408}{0.85} = \dfrac{40800}{85}$.
• $85 \times 480 = 40800$, so $P = 480$.

So, after the first discount (but before the 15% discount), the laptop cost $480$.

The laptop originally cost $600$ and was reduced to $480$ after the first discount.

Amount of the first discount:

$600 - 480 = 120$ dollars.

So the first discount lowered the price by $120$ from the original $600$.

The first discount is $120$ out of the original $600$.

The fraction of the original price that was discounted is:

$\dfrac{120}{600} = 0.20 = 20\\%$.

Therefore, $x = 20\\%$.