Questions: Amanda and her husband are each starting a saving plan. Amanda will initially set aside 650 and then add 165 every month to the savings. The amount A (in dollars) saved this way is given by the function A=650+165N, where N is the number of months she has been saving.
Her husband will not set an initial amount aside but will add 385 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=385N.
Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.
Transcript text: Amanda and her husband are each starting a saving plan. Amanda will initially set aside $\$ 650$ and then add $\$ 165$ every month to the savings. The amount $A$ (in dollars) saved this way is given by the function $A=650+165 N$, where $N$ is the number of months she has been saving.
Her husband will not set an initial amount aside but will add $\$ 385$ to the savings every month. The amount $B$ (in dollars) saved using this plan is given by the function $B=385 N$.
Let $T$ be total amount (in dollars) saved using both plans combined. Write an equation relating $T$ to $N$. Simplify your answer as much as possible.
Solution
Solution Steps
Step 1: Define the Savings Functions
Amanda's savings after \( N \) months is given by the function:
\[
A = 650 + 165N
\]
Her husband's savings after \( N \) months is given by the function:
\[
B = 385N
\]
Step 2: Calculate Total Savings
The total savings \( T \) after \( N \) months can be expressed as:
\[
T = A + B = (650 + 165N) + (385N)
\]
Step 3: Simplify the Total Savings Equation
Combining the terms, we have:
\[
T = 650 + (165 + 385)N = 650 + 550N
\]
Step 4: Calculate Total Savings for \( N = 5 \)
Substituting \( N = 5 \) into the simplified total savings equation:
\[
T = 650 + 550 \times 5 = 650 + 2750 = 3400
\]
Final Answer
The total savings after 5 months is:
\[
\boxed{T = 3400}
\]