Original Price

[nycmath]

Let D = dollars

The original price of an item is discounted 20%. A customer buys the item at this discounted price using a 20D-off coupon. There is no tax on the item, and this was the only item the customer bought. If the customer paid 1D and 90 cents more than half the original price of the item, what was the original price of the item?

[Eigenvalue]

Let the original price of the item be x

List the steps:
1. The item is discounted at 20% off
The price is (1-0.2)x, or 0.8x

2. 20 dollar off coupon
0.8x-20

Set the expression equal to the final price of the item:
0.8x-20=1.9+0.5x
0.3x=21.9
3x=219
x=73

The item cost $73

[nycmath]

Let the original price of the item be x

List the steps:
1. The item is discounted at 20% off
The price is (1-0.2)x, or 0.8x

2. 20 dollar off coupon
0.8x-20

Set the expression equal to the final price of the item:
0.8x-20=1.9+0.5x
0.3x=21.9
3x=219
x=73

The item cost $73

A nice setup leading to the right answer.