Diane and her husband are each starting a saving plan. Diane will initially set aside and then add every month to the savings. The amount (in
dollars) saved this way is given by the function , where is the number of months she has been saving.
Her husband will not set an initial amount aside but will add to the savings every month. The amount (in dollars) saved using this plan is given by the
function .
Let be total amount (in dollars) saved using both plans combined. Write an equation relating to . Simplify your answer as much as possible.

Ask by Brooks Stephens. in the United States

Jan 23,2025

Question

Diane and her husband are each starting a saving plan. Diane will initially set aside and then add every month to the savings. The amount (in
dollars) saved this way is given by the function , where is the number of months she has been saving.
Her husband will not set an initial amount aside but will add to the savings every month. The amount (in dollars) saved using this plan is given by the
function .
Let be total amount (in dollars) saved using both plans combined. Write an equation relating to . Simplify your answer as much as possible.

Ask by Brooks Stephens. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

To find the total amount $$ T $$ saved by both Diane and her husband, we can add their individual savings functions.

1. **Diane's Savings:**
   $$
   A = 145N + 750
   $$
   - **Initial amount:** \$750
   - **Monthly addition:** \$145

2. **Husband's Savings:**
   $$
   B = 385N
   $$
   - **Initial amount:** \$0
   - **Monthly addition:** \$385

3. **Total Savings $$ T $$:**
   $$
   T = A + B
   $$
   Substitute the expressions for $$ A $$ and $$ B $$:
   $$
   T = (145N + 750) + 385N
   $$
   Combine like terms:
   $$
   T = (145N + 385N) + 750
   $$
   $$
   T = 530N + 750
   $$

**Final Equation:**
$$
T = 530N + 750
$$
The total amount saved $$ T $$ is given by the equation: $$ T = 530N + 750 $$

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