# You buy a bicycle helmet for Thinking $22.26, which includes 6% sales tax. The helmet is discounted 30% off the selling price. What is the original price? ##### 1 Answer Aug 20, 2017 See a solution process below: #### Explanation: First, we need to determine the amount of the sales tax. We can use this formula: $c = p + \left(p \cdot t\right)$Where: $c$is the total cost paid,$22.26 for this problem.

$p$ is the price paid before tax, what we will solve for.

$t$ is the tax rate, 6% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 6% can be written as $\frac{6}{100}$.

Substituting and solving for $p$ gives:

$22.26 = p + (p * 6/100) $22.26 = (100/100 * p) + (6p)/100

$22.26 = (100p)/100 + (6p)/100 $22.26 = (106p)/100

color(red)(100)/color(blue)(106) * $22.26 = color(red)(100)/color(blue)(106) xx (106p)/100 ($2226)/color(blue)(106) = cancel(color(red)(100))/cancel(color(blue)(106)) xx (color(blue)(cancel(color(black)(106)))p)/color(red)(cancel(color(black)(100)))

$21.00 = p Now that we know the price we paid before taxes, we can determine the original price of the helmet before the discount use a very similar formula: $p = l - \left(l \cdot d\right)$Where: $p$is the price paid before taxes which we solved for above as$21

$l$ is the original list price of the helmet - what we are solving for in this problem.

$d$ is the discount rate - 30% in this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 30% can be written as $\frac{30}{100}$.

Substituting and solving for $l$ gives:

$21 = l - (l * 30/100) $21 = (100/100 * l) - (30l)/100

$21 = (100l)/100 - (30l)/100 $21 = (70l)/100

color(red)(100)/color(blue)(70) * $21 = color(red)(100)/color(blue)(70) * (70l)/100 ($2100)/color(blue)(70) = cancel(color(red)(100))/cancel(color(blue)(70)) * (color(blue)(cancel(color(black)(70)))l)/color(red)(cancel(color(black)(100)))

$30 = l l =$30

The original price of the helmet is \$30.