Relationships between Percentage change and inversely proportional numbers

J

Jmq10

New member
Joined
Jun 30, 2020
Messages
3
Hi, I've got a problem that i can't get my head around. I've been given an hourly rate based on a total number of hours.
Assumed total hours 350
Rate $49 per hour.
As the hours go down the rate goes up.
I've only used 258 hours therefore I'm trying to figure out the new rate. If I use the inverse proportional rules, I get (350/258)×49= 66.47
However, if I look at the percentage change in hours it's (258-350)/350=-26%
I would have though that the rate should be 26% higher but this comes out with a different answer. Can someone explain the differences in the two methods and why they don't agree. Am I comparing two separate things. I thought if the hours were a fifth less the rate would also be a fifth less. It doesn't work that way unless the hours are halved, therefore the rate is doubled.
 
Jmq10 said:
Hi, I've got a problem that i can't get my head around. I've been given an hourly rate based on a total number of hours.
Assumed total hours 350
Rate $49 per hour.
As the hours go down the rate goes up.
I've only used 258 hours therefore I'm trying to figure out the new rate. If I use the inverse proportional rules, I get (350/258)×49= 66.47
However, if I look at the percentage change in hours it's (258-350)/350=-26%
I would have though that the rate should be 26% higher but this comes out with a different answer. Can someone explain the differences in the two methods and why they don't agree. Am I comparing two separate things. I thought if the hours were a fifth less the rate would also be a fifth less. It doesn't work that way unless the hours are halved, therefore the rate is doubled.
Click to expand...
Are you assuming that your TOTAL pay will remain same?
 
It seems odd that the rate would be inversely proportional to hours worked, which implies a fixed total amount, and I'd expect them to just say that directly. I'd like to see the actual wording of the arrangement. But I'll assume you're right.

Percent change works very differently from proportions, so what you found is to be expected. Essentially, percent change is a matter of addition and subtraction, while proportion is a matter of multiplication and division. Here's one way to think about it.

Suppose, to keep the numbers simple, your hours decrease by 25%. That means the number of hours is 75% of what it was; it's multiplied by 0.75 (that is, 3/4).

To compensate, the rate would be divided by 0.75. This is the same as being multiplied by 1/0.75 = 1.333... (that is, 4/3). So the rate is increased by 33.3%. This is not the same as 25%.

Similarly, if the hours decreased by 20% (1/5), they would be multiplied by 80% (4/5); so the rate would be divided by 80% (multiplied by 5/4 = 1.25), so it would increase by 25%. This is just the way things work.
 
Jmq10 said:
Hi, I've got a problem that i can't get my head around. I've been given an hourly rate based on a total number of hours.
Assumed total hours 350
Rate $49 per hour.
As the hours go down the rate goes up.
I've only used 258 hours therefore I'm trying to figure out the new rate. If I use the inverse proportional rules, I get (350/258)×49= 66.47
However, if I look at the percentage change in hours it's (258-350)/350=-26%
I would have though that the rate should be 26% higher but this comes out with a different answer. Can someone explain the differences in the two methods and why they don't agree. Am I comparing two separate things. I thought if the hours were a fifth less the rate would also be a fifth less. It doesn't work that way unless the hours are halved, therefore the rate is doubled.
Click to expand...
You haven't told us how the rate changes. It goes up how??
 
You must log in or register to reply here.
Top