Answers:
a. Write an expression that shows the regular price r for a t-shirt minus the $5 discount
Expression=r-$5
b. Write a rule for the function p(r) that expresses the final price p of a t-shirt with the with the discount applied and sales tax added.
p(r)=1.05(r-$5)
c. How much would you pay during Bargain Days for a shirt regularly priced at $15.50?
You would pay $11.03 during Bargain Days for a shirt regularly priced at $15.50.
Solution:
a. Write an expression that shows the regular price r for a t-shirt minus the $5 discount.
Regular price: r
Discount: $5
Expression=r-$5
b. Write a rule for the function p(r) that expresses the final price p of a t-shirt with the with the discount applied and sales tax added.
Final price: p(r)
There is a state sales tax of 5%, and The $5 discount is applied before the sales tax is calculated:
p(r)=Expression+Sales tax
State sales tax=5%=5/100→State sales tax=0.05
Sales tax=State sales tax * Expression
Sales tax=0.05*Expression
p(r)=Expression+0.05*Expression
p(r)=(1+0.05)*Expression
p(r)=1.05*Expression
Expression=r-$5
p(r)=1.05(r-$5)
c. How much would you pay during Bargain Days for a shirt regularly priced at $15.50?
r=$15.50→p(r)=p($15.50)
p($15.50)=1.05($15.50-$5)
p($15.50)=1.05($10.50)
p($15.50)=$11.025
p($15.50)=$11.03
You would pay $11.03 during Bargain Days for a shirt regularly priced at $15.50.
