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Combining functions to write a new function that models a real-world situation Example: Amanda and her husband are each starting a saving plan. Amanda will initially set aside $250 and then add $145 every month to the savings. The amount A (in dollars) saved this way is given by the function A = 145N+250, where N is the number of months she has been saving. Her husband will not set an initial amount aside but will add $495 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B = 495N. 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. - Explanation: I The most important two things to solve this type of problems correctly are; 1. You need to be very careful and check whether you are asked to add or subtract the expressions 2. Be very careful with the signs and combining like terms. . . . . . . . . . . . When you are asked to find the total you add When you are asked to find the profit or when you compare you subtract . . . . . The total amount T (in dollars) saved using both plans combined is given by the following. T = Savings for Amanda + Savings for her husband = A+B We're given that A = 145N+250 and B = 495N. So here is what we get. T= 145N+250+495N = 145/+250+495/ Identifying like terms - 250 Simplifying Related Topics: Writing an equation and graphing a line given its slope and -Intercept Self Evaluation: WWWWWA car rental company charges an initial fee plus an additional fee for each mile driven. The charge depends on the type of car: economy or luxury. The charge E (in dollars) to rent an economy car is given by the function E = 0.70M+ 10.95, where Mis the number of miles driven. The charge L (in dollars) to rent a luxury car is given by the function L = 1.05M7L 17.30. Let C be how much more it costs to rent a luxury car than an economy car (in dollars). Write an equation relating C to M Simplify your answer as much as possible. C = ' X S