The formula for calculating the total cost of an item with tax is:
#p = c + (c * t)# or, factoring out a #c#: #p = c(1 + t)#
Where:
#p# is the total price - $26.99 for this problem.
#c# is the cost of the item before taxes - $24.99 for this problem.
#t# is the tax rate or percent - we will call it #t%# for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore t% can be written as #t/100#.
Substituting and solving for #t# gives:
#$26.99 = $24.99(1 + t/100)#
#($26.99)/color(red)($24.99) = ($24.99(1 + t/100))/color(red)($24.99)#
#(color(red)(cancel(color(black)($)))26.99)/color(red)(color(black)(cancel(color(red)($)))24.99) = (color(red)(cancel(color(black)($24.99)))(1 + t/100))/cancel(color(red)($24.99))#
#26.99/color(red)(24.99) = 1 + t/100#
#1.08 = 1 + t/100#
#-color(red)(1) + 1.08 = -color(red)(1) + 1 + t/100#
#0.08 = 0 + t/100#
#0.08 = t/100#
#color(red)(100) xx 0.08 = color(red)(100) xx t/100#
#8 = cancel(color(red)(100)) xx t/color(red)(cancel(color(black)(100)))#
#8 = t#
#t = 8#
The tax rate is #color(red)(8%)#
