A bicycle helmet has a selling price of $50. The helmet is discounted 30% off the selling price. The sales tax rate is 6%. What is the total cost of the helmet?

See a solution process below:

Explanation:

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

)

+

6

p

100

$

22.26

=

100

p

100

+

6

p

100

$

22.26

=

106

p

100

100

106

⋅

$

22.26

=

100

106

×

106

p

100

$

2226

106

=

100

106

×

106

p

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

)

−

30

l

100

$

21

=

100

l

100

−

30

l

100

$

21

=

70

l

100

100

70

⋅

$

21

=

100

70

⋅

70

l

100

$

2100

70

=

100

70

⋅

70

l

100

$

30

=

l

l

=

$

30

The original price of the helmet is $30.

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step-by-step explanation: