Diane and her husband are each starting a saving plan. Diane will initially set aside \( \$ 750 \) and then add \( \$ 145 \) every month to the savings. The amount \( A \) (in dollars) saved this way is given by the function \( A=145 N+750 \), 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 \( B=385 \mathrm{~N} \). 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. \( T=T \)

To find the total amount \( T \) saved using both Diane's and her husband's plans, we can combine their savings functions. The total savings is represented by the equation: \[ T = A + B \] Substituting the functions for \( A \) and \( B \): \[ T = (145N + 750) + (385N) \] Now, combine like terms: \[ T = 145N + 385N + 750 \] \[ T = 530N + 750 \] So the total amount saved after \( N \) months is given by \( T = 530N + 750 \). Now we have a clear understanding of how their savings contribute over time. Saving plans like this can teach great lessons about financial growth and how initial investments, combined with consistent contributions, can lead to substantial savings over time. A little planning goes a long way! Both Diane and her husband are setting themselves up for success! In real life, having a savings plan can save you from those “oops” moments when unexpected expenses pop up. Regular contributions can make a difference, so consider setting one up for your financial goals!