All variation problems start out as
The NUMERATOR consists of
either 1. the "directly" variable.
or 2. the product of all directly or jointly variables, if more than one.
or 3. the number 1 if there are no directly or jointly variables.
The DENOMINATOR consists of
either 1. the "inversely" variable.
or 2. the product of all "inversely" variables, if more than one.
or 3. the number 1 if there are no "inversely" variables.
You should memorize the above.
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Write a linear function that relates the monthly payment p to the amount
borrowed b for a mortgage with the same terms.
The monthly payment p on a mortgage varies...
That's the VARYING VARIABLE. That is, p.
...directly with the amount B.
So the NUMERATOR is B
Since there are no "inversely" variables, the DENOMINATOR is 1
So we have
That equation would be the answer if we had a number to put for k. So we'll
find the number to put for k.
You decide to borrow $130,000. ...
You are told that your payment is $813.
Therefore we substitute $813 for p and 130000 for B
Divide both sides by 130000 to solve for k
We now go back to
and substitute 0.006253462 for k:
That equation is the answer. It is a linear function that relates the monthly
payment p to the amount borrowed B for a mortgage with the same terms.
Edwin