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.

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.
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Solution

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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: \[ \boxed{T = 3400} \]

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