Sonoko ordered a howl of pcnne pasta in pesto sauce for 15 a

Sonoko ordered a howl of pcnne pasta in pesto sauce for $15 and Janice\'c choice was a bowl of gnocchi in gorgonzola sauce with spinach and toasted walnuts that costed $17. To celebrate this very special occasion the girls shared a piece of Presto Panini\'s famous tiramisu ($8) and a 1/2 litter of Chianti ($20.) In Nova Scotia sales taxes applied to foodservice are calculated as a single tax, called the Harmonized Sales Tax (HST), of 15% of the total food and beverage purchase. Since as an undergraduate student she used to work as a waitress, Sonoko is a very generous tipper. Her tipping policy is to give 8/5, the ratio of the sixth and the fifth terms of the Fibonacci sequence, of the HST amount to the server. (a) What was the amount of the HST on Sonoko and Janice\'s bill? (b) What was the tip that Sonoko left for the server? (c) Suppose that x is the amount in dollars of the total food and beverage purchase. Let h(x) be the function that associates the amount of the HST to the amount x. Find an expression for h(x). (d) Let f(t) = 8/5 middot t. Express Sonoko\'s tipping policy in terms of the functions h and f.

Solution

solution:

a) amount of total bill = sum of the food items purchased + hst onn total amount

sum of amount of items purchased= 15+17+8+20 =60$

hst= 15% of 60 =9$

amount of total bill=60+9 = 69$

b) amount left to the server = (8/5)*(hst amount)

= 8*9/5=14.4$

c) h(x)=0.15 x

d) amount to server

=  (8/5)*(hst amount)

= (8/5)*(0.15x)

=0.24x

and

f=(8/5)t

f(x)=8x/5

now

tipping policy

=(8/5)*(0.15x)

but

f(x)=8x/5

hencee tipping policy interms of f

=0.15f