Question

Pablo and his wife are each starting a saving plan. Pablo will initially set aside $50 and then add $40.75 every week to the savings. The amount A (in dollars) saved this way is given by the function A=50+40.75N, where N is the number of weeks he has been saving. His wife will not set an initial amount aside but will add $60.75 to the savings every week. The amount B (in dollars) saved using this plan is given by the function B=60.75N. Let I be total amount (in dollars) saved using both plans combined. Write an equation relating I to N. Simplify your answer as much as possible.​

Answer 1

The equation relating the total amount saved (I) to the number of weeks (N) for both Pablo and his wife is I = 50 + 101.5N.

Explanation:

To find the equation relating the total amount saved (I) to the number of weeks (N) for both Pablo and his wife, we need to add the amounts saved by each person.

For Pablo, the amount saved (A) is given by the function A = 50 + 40.75N, where N is the number of weeks. This means that after 1 week, Pablo will have saved $50 + $40.75, after 2 weeks, he will have saved $50 + 2($40.75), and so on.

For his wife, the amount saved (B) is given by the function B = 60.75N. This means that after 1 week, his wife will have saved $60.75, after 2 weeks, she will have saved 2($60.75), and so on.

To find the total amount saved (I) by both of them combined, we need to add the amounts saved by Pablo and his wife:

I = A + B

Substituting the given functions:

I = (50 + 40.75N) + (60.75N)

Simplifying, we combine like terms:

I = 50 + 40.75N + 60.75N

I = 50 + (40.75 + 60.75)N

I = 50 + 101.5N

So, the equation relating the total amount saved (I) to the number of weeks (N) for both Pablo and his wife is I = 50 + 101.5N.