First, we need to determine the amount of the sales tax. We can use this formula:
#c = p + (p * t)#
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 #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 - (l * d)#
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 #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.
