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Sandra bought a new computer for $\$600$ and is paying on an installment plan. She paid $\$100$ at the time of purchase and will make $\$50$ payments each month until the computer is paid off. The function $C(p)$ represents the amount Sandra owes on the computer after making $p$ payments of $\$50$ . What is the domain of $C(p)$ ? $\newline$ Choices: $\newline$ (A) all whole numbers $\newline$ (B) all whole numbers from $0$ to $10$ $\newline$ (C) all whole numbers from $0$ to $50$ $\newline$ (D) all whole numbers from $0$ to $600$

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Domain and range of linear functions: word problems

Full solution

Q. Sandra bought a new computer for

\$600

and is paying on an installment plan. She paid

\$100

at the time of purchase and will make

\$50

payments each month until the computer is paid off. The function

C(p)

represents the amount Sandra owes on the computer after making

p

payments of

\$50

. What is the domain of

C(p)

?

\newline

Choices:

\newline

(A) all whole numbers

\newline

(B) all whole numbers from

0

to

10

\newline

(C) all whole numbers from

0

to

50

\newline

(D) all whole numbers from

0

to

600

Initial Payment Calculation: Sandra's initial payment is \\(100\), and the total cost of the computer is \$\(600\). To find out how much she still owes after the initial payment, we subtract the initial payment from the total cost.\(\newline\)Calculation: \$\(600\) - \$\(100\) = \$\(500\)\(\newline\)Sandra owes \$\(500\) after the initial payment.
Monthly Payment Calculation: Each month, Sandra makes a payment of \(\$50\). To find out how many payments she will need to make to pay off the \(\$500\), we divide the remaining amount by the monthly payment amount.\(\newline\)Calculation: \(\$500 / \$50 = 10\)\(\newline\)Sandra needs to make \(10\) payments of \(\$50\) each to pay off the computer.
Domain of C(p): The domain of C(p) is the set of all possible values that p (the number of \(50) payments) can take. Since Sandra can make from \$0\) payments (before she starts paying off the computer) to \(10\) payments (to pay it off completely), the domain is all whole numbers from \(0\) to \(10\).

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