Math word question calculus

needhelpmath2000

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I am having hard time understanding this question. any help would be great. My understanding is that total loan is 217.39x that would to be paid off in 25 years (300 payments) and you also can afford down payment?? of 30,000 but help would be great.


Suppose a payment of X dollars per month pays of a loan of 217.39X dollars in 25 years and that you have cash on hand in the amount of $30,000. You plan on buying a house.
(a) Express the house price you can afford as a function of the monthly mortgage payment you can afford and vice versa.
(b) You are considering to use 6R dollars for renovation costs (assume 6R <= 30; 000). If you keep the same monthly mortgage payment,
in percentage terms, how much does the house price you can afford decrease?


so far:

Total can afford= 217.39x+30,000
Total payments= 300x-(30,000/(217.39x))
 
Suppose a payment of X dollars per month pays of a loan of 217.39X dollars in 25 years and that you have cash on hand in the amount of $30,000. You plan on buying a house.
(a) Express the house price you can afford as a function of the monthly mortgage payment you can afford and vice versa.
By "and vice versa", I think they mean "and also express the payment you can afford as a function of the house price you can afford".

From back in algebra, you'll need to start by picking a function name, so that you can write the relationship as a function. What function name are you picking?

Total can afford= 217.39x+30,000
Total payments= 300x-(30,000/(217.39x))
By the above, do you mean that you picked a function name, such as "h" (for "house that I can afford"), so that the relationships, as functions, are:

. . . . .house "h" as a function of monthly payment "x":

. . . . .h(x) = 217.39x + 30,000


. . . . .monthly payment "x" as a function of house "h":

. . . . .x(h) = 300h - (30,000/217.39h)

If so, then I think the first function is valid, but I'm not seeing how you get the second function. Please reply with a clear listing of your reasoning and steps.

(b) You are considering to use 6R dollars for renovation costs (assume 6R <= 30; 000). If you keep the same monthly mortgage payment, in percentage terms, how much does the house price you can afford decrease?
The 6R is going to be subtracted from the 30,000, so that your down-payment is going to be 30,000 - 6R. You used to be able to afford this much house:

. . . . .h(x) = 271.39x + 30,000

What expression stands for how much house can you afford now? What fractional expression stands for the percentage that this new amount is of the old amount? If you subtract this amount from 1 (for "100% of the old amount"), what is the amount of decrease?

Note: I see no way of obtaining numerical values for this part of the exercise. ;)
 
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