Question

3. The minimum payment on a credit card is based on the total amount owed. A credit card company uses
the following rules: For a bill less than $20 the entire amount is due, for a bill of at least $20 but less than
$500, the minimum due is $20. For a bill of at least $500 but less than $ 1000 the minimum due is $40 and
for a bill of at least $1000 but less than $ 1500 the minimum due is $80 dollars. For a bill of $1500 or more
the minimum due is = of the bill.
a. Write a function to describe the minimum payment due.
b. What is the minimum payment due if the bill is $345?
c. What is the minimum payment due if the bill is $1410?
d. What is the minimum payment due if the bill is $1700?

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The minimum payment on a credit card is based on the total amount owed. A credit card company uses the following rules: For a bill less than $20 the entire amount is due, for a bill of at least $20 but less than $500, the minimum due is $20. For a bill of at least $500 but less than $1000 the minimum due is $40 and for a bill of at least $1000 but less than $1500 the minimum due is $80 dollars. For a bill of $1500 or more the minimum due is 1/10th of the bill.

a. Write a function to describe the minimum payment due.  

b. What is the minimum payment due if the bill is $345?  

c. What is the minimum payment due if the bill is $1410?  

d. What is the minimum payment due if the bill is $1700?

Solution:

Let B represent the minimum due payment for a bill in dollars and let x represent the bill in dollars. Therefore:

For x < 20, B = x

For 20 ≤ x < 500, B = 20

For 500 ≤ x < 1000, B = 40

For 1000 ≤ x < 1500, B = 80

For x ≥ 1500, B = (1/10)x

a)

$B(x)=\left \{ {{x\ \ \ x<20} \atop {20\ \ 20\leq x<500\\\atop {40\ \ \ 500\leq x<1000\\\atop {80\ \ \ 1000\leq x<1500\\\atop {\frac{1}{10}x \ \ \ x>1500}}} }} \right.$

b) For 20 ≤ x < 500, B = 20

Therefore if the bill is $345 (x = 345), the minimum payment due would be $20

c) For 1000 ≤ x < 1500, B = 80

Therefore if the bill is $1410 (x = 1410), the minimum payment due would be $80

d) For x ≥ 1500, B = (1/10)x

Therefore if the bill is $1700 (x = 1700), the minimum payment due would be $170 (1/10 * 1700)