Question: 1. John bought a bicycle on sale for $172.47 including 7.12 tax. If the bike was 30% off, how much…

1. John bought a bicycle on sale for $172.47 including 7.12 tax. If the bike was 30% off, how much was the original price before tax? Round it to dollar amount.

Solution

John bought a bicycle on sale for $172.47, including 7.12% tax. The bike was 30% off. We need to find the original price before tax, rounded to the nearest dollar. Let the original price before discount be \( x \). The price after a 30% discount is \( 0.7x \). Including 7.12% tax, the equation is: \[ 1.0712 \times 0.7x = 172.47 \] Divide both sides by \( 1.0712 \) to find \( 0.7x \): \[ 0.7x = \frac{172.47}{1.0712} \] Calculate the right side: \[ 0.7x \approx 160.97 \] Now, divide by 0.7