Cheryl purchased 5 identical hollow pine doors and 6 identical solid oak doors for the house she is building. The regular price of each solid oak door was twice the regular price of each hollow pine?

You started by correctly identifying that the original price ratio of the hollow pine door to the solid oak door is 1:2, with prices of $40 and $80, respectively.

However, the mistake happens when you try to adjust the ratio after applying the 25% discount. You calculated that the final ratio should be 1:1.75 and that this implies a new price of $70 for the solid oak door. This step is where things go wrong.

Here’s why:

1. Discount Application: The problem states that Cheryl received a 25% discount on the solid oak doors. This means you should reduce the original $80 price by 25%, which gives you $60, not $70. The correct calculation is:
   80 × (1 - 0.25) = 80 × 0.75 = 60 dollars
   So, the price after the discount is fixed at $60.

2. Incorrect Ratio Adjustment: The ratio of 1:1.75 that you used isn't necessary here. The discount simply reduces the price to $60, and we should work with that exact price. Adjusting to $70 based on the ratio leads to an incorrect total cost because it doesn’t reflect the actual 25% discount.

Correct Total Price:
When you use the correct discounted price of $60 for the solid oak doors, the total cost becomes:
5 × 40 + 6 × 60 = 200 + 360 = 560 dollars

I hope this helps :)