Evaluating Composite Functions in Real-Life Scenarios

1. A car rental company charges a base fee of $30 plus $0.20 per mile driven. If the function C(m) represents the total cost for m miles driven, and the function D(c) represents the number of days rented based on the total cost, find D(C(100)) if the daily rental fee is $50.

• 5

• 3

• 1

• 2

2. A bakery sells cupcakes for $2 each and offers a discount function D(n) that gives a $5 discount for every 10 cupcakes purchased. If the function T(n) represents the total cost for n cupcakes, evaluate T(D(20)).

• 40

• 25

• 30

• 35

3. A gym charges a monthly fee of $40 and an additional $10 for each class attended. If the function G(c) represents the total cost for attending c classes, and the function M(g) represents the number of months based on the total cost, find M(G(5)).

• 4

• 3

• 2

• 1

4. A phone plan costs $25 per month plus $0.10 per text message sent. If the function P(t) represents the total cost for t text messages, and the function S(p) represents the number of months based on the total cost, evaluate S(P(50)).

• 0.8 months

• 2.0 months

• 1.2 months

• 1.5 months

5. A landscaping service charges a flat fee of $100 plus $15 per hour of work. If the function L(h) represents the total cost for h hours of work, and the function R(l) represents the number of jobs based on the total cost, find R(L(4)).

• 8

• 12

• 10

• 5

6. A subscription service charges $15 per month and an additional fee of $2 for every movie rented. If the function S(m) represents the total cost for renting m movies, and the function N(s) represents the number of months based on the total cost, evaluate N(S(10)).

• 15

• 10

• 20

• 5

7. A delivery service charges a base fee of $5 plus $0.50 per mile. If the function F(d) represents the total cost for d miles, and the function T(f) represents the time taken based on the total cost, find T(F(20)).

• T(F(20)) equals $15.

• Insufficient information to determine T(15).

• T(F(20)) is $10.

• T(F(20)) cannot be calculated.

8. A concert ticket costs $50, and there is a service fee of $10 per ticket. If the function C(t) represents the total cost for t tickets, and the function A(c) represents the number of concerts based on the total cost, evaluate A(C(3)).

• 5

• 3

• 4

• 2

9. A tutoring service charges $25 per hour and offers a package deal of 5 hours for $100. If the function P(h) represents the total cost for h hours, and the function Q(p) represents the number of packages based on the total cost, find Q(P(10)).

• 1.5

• 2.5

• 4.0

• 3.0

10. A subscription box service charges $20 per box and an additional shipping fee of $5. If the function B(n) represents the total cost for n boxes, and the function C(b) represents the number of months based on the total cost, evaluate C(B(4)).

• $30

• $25

• $15

• 1 month