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Betty has a checking account and a non-interest-bearing savings account. Function [tex]\( C \)[/tex] represents her checking account balance, where [tex]\( x \)[/tex] is the number of months. Function [tex]\( S \)[/tex] represents her savings account balance.

[tex]\[
\begin{aligned}
C(x) &= -|240x - 140| + 1,400 \\
S(x) &= 450x + 100
\end{aligned}
\][/tex]

Which function represents Betty's total account balance, [tex]\( T(x) \)[/tex]?

A. [tex]\( T(x) = -|240x - 140| + 450x + 1,400 \)[/tex]

B. [tex]\( T(x) = |240x + 140| + 450x + 1,500 \)[/tex]

C. [tex]\( T(x) = -|240x - 140| + 450x + 1,500 \)[/tex]

D. [tex]\( T(x) = -|240x - 140| + 450x + 1,300 \)[/tex]



Answer :

GinnyAnswer
To solve this question, we need to find a function that represents Betty's total account balance, [tex]\(T(x)\)[/tex], by summing the balances of her checking account and savings account over time [tex]\(x\)[/tex] months.

Betty's checking account balance is given by:
[tex]\[ C(x) = -|240x - 140| + 1,400 \][/tex]

Betty's savings account balance is given by:
[tex]\[ S(x) = 450x + 100 \][/tex]

The total account balance is the sum of these two functions:
[tex]\[ T(x) = C(x) + S(x) \][/tex]

Substituting [tex]\(C(x)\)[/tex] and [tex]\(S(x)\)[/tex] into [tex]\(T(x)\)[/tex]:
[tex]\[ T(x) = (-|240x - 140| + 1,400) + (450x + 100) \][/tex]

Now, combine like terms:
[tex]\[ T(x) = -|240x - 140| + 1,400 + 450x + 100 \][/tex]
[tex]\[ T(x) = -|240x - 140| + 450x + 1,500 \][/tex]

Therefore, the function that represents Betty’s total account balance [tex]\(T(x)\)[/tex] is:
[tex]\[ T(x) = -|240x - 140| + 450x + 1,500 \][/tex]

Comparing with the given options:
- Option A: [tex]\(T(x) = -|240x - 140| + 450x + 1,400\)[/tex]
- Option B: [tex]\(T(x) = |240x + 140| + 450x + 1,500\)[/tex]
- Option C: [tex]\(T(x) = -|240x - 140| + 450x + 1,500\)[/tex]
- Option D: [tex]\(T(x) = -|240x - 140| + 450x + 1,300\)[/tex]

The correct answer is:
[tex]\[ \boxed{C} \][/tex]

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