Let's solve the problem step-by-step to find the current price of a stereo set that originally cost [tex]$189, taking into consideration the discounts applied in sequence.
1. Initial Price:
The original price of the stereo set is $[/tex]189.
2. First Discount:
The first discount applied is 10%.
To find the new price after this discount, we calculate 10% of [tex]$189 and subtract it from the original price.
\[
\text{First discount} = 189 \times 0.10 = 18.90
\]
Then, subtract this discount from the original price:
\[
\text{Price after first discount} = 189 - 18.90 = 170.10
\]
3. Second Discount:
The second discount is 25% off the price obtained after the first discount.
To find the new price after this second discount, we calculate 25% of $[/tex]170.10 and subtract it from the price after the first discount.
[tex]\[
\text{Second discount} = 170.10 \times 0.25 = 42.525
\][/tex]
Then, subtract this discount from the price after the first discount:
[tex]\[
\text{Final price} = 170.10 - 42.525 = 127.575
\][/tex]
Therefore, the current price of the stereo set after both discounts is approximately $127.58 (rounded to two decimal places).
