all other things being equal, i think it will be a straight ratio to find the larger payment.
i checked with an online calculator to see if that was true.
it was.
here's the results of my finding.
first i found the interest rate.
then i changed the present value to 90,000 from 54,000.
the monthly payment for the 90,000 dollar loan was 90/54 * 450.75 = 751.25, confirming the ratio formula worked as long as the number of payments remained the same and the interest rate remained the same.
it appears the monthly payment is directly proportional to the amount of the investment as long as all other factors remain the same.
with direct propportion, the formula is y = k * x
when y = 54000 and x = 450.75, solve for k to get:
k = 54000 / 450.75.
when y = 90000 and k = 54000 / 450.75, the formula becomes:
90000 = 54000 / 450.75 * x
solve for x to get:
x = 90000 / (54000 / 450.75) = 90000 * 450.75 / 54000 = 751.25.
thirty workers finish in 25 days.
25 workers, working at the same rate, should finish in 25/30 * 25 = 20.833333..... days.
i used the rate * people * time = quantity formula to see what the relationship would be.
with 30 workers, the formula becomes rate * 30 * 25 = 1
the rate is the rate that each person works at.
people is the number of people involved.
time is how long it takes.
1 = the quantity, which is one finished house.
solve for rate to get:
rate = 1/(30*25) = 1/750.
this says that each person can finish 1/750 of the house in 1 day.
with 30 people, then all 30 can finish 1/25 of the house in 1 day.
the whole house can then be finished in 25 days.
the rate of each person is 1/750 of the house in one day.
this remains the same.
the formula for 30 people becomes 1/750 * 30 * 25 = 1
1/750 is the rate of each person.
30 is the number of people.
25 is the number of days.
1 is the quantity of work performed.
evaluate the equation to get 1 = 1, confirming the values are good.
when the rate of each person remains the same and the number of people becomes 25 instead of 30, the formula becomes:
1/750 * 25 * number of days = 1
solve for number of days to get:
number of days = 1/(1/750 * 25) = 1/(25/750) = 1*750/25 = 30
1/750 is the rate of each person.
25 is the number of people.
30 is the number of days.
1 is the quantity of work performed.
it appears like the number of days is inversely proportional to the number of workers as long as all other factors remain the same.
the inverse proportion formula is y = k/x
when y = number of days and x = number of workers, the formula becomes:
25 = k/30
solve for k to get:
k = 750.
when x = 25, the formula becomes:
y = 750/25.
solve for y to get:
y = 30.
the relationship between the direct and inverse proportion formulas is not that easy to see, which is why i always go to the basic formulas of:
rate * time = quantity.
rate * number of people * time = quantity.
when number of people are involved, i use the rate * number of people * time = quantity formula.
when number of people are not involved, i use the rate * time = quantity formula.
if i really think about it, .....
assuming people are involved, the formula is:
rate * number of people * time = quantity.
assuming rate and quantity are always the same, then solve for number of people * time to get:
number of people * time = quantity / rate.
since quantity / rate is always the same, then set it equal to k.
formula becomes:
number of people * time = k
solve for time to get time = k / number of people.
solve for number of people to get number of people = k / time.
both of these are inverse ratio type problems.
i never really connected it this way before, but it makes sense, and confirms that the relationship is an inverse relationship.