Barbra has a coupon for 5% off of the cost of her dinner, She tips the waiter 20% of the discounted priice of her dinner, and pays a total (discounted dinner price + tip) of $18.24, how much did her dinner cost before the discount?
To find out how much Barbra's dinner cost before the discount, we need to work backwards from the total amount she paid.
Let's start by assuming the original cost of her dinner is represented by 'x'.
According to the question, Barbra has a coupon for 5% off, so after applying the discount, the cost of her dinner would be (x - 0.05x) = 0.95x.
Next, Barbra tips the waiter 20% of the discounted price, which means she pays an additional 0.20 * 0.95x = 0.19x as a tip.
Therefore, the total amount she paid (discounted dinner price + tip) is 0.95x + 0.19x = 18.24.
Adding the like terms on the left side of the equation, we have 1.14x = 18.24.
Now, to find the value of 'x', we need to divide both sides of the equation by 1.14:
x = 18.24 / 1.14
x ≈ 16
Therefore, Barbra's dinner cost before the discount was approximately $16.