Dimensional analysis homework help?

Question

Because you never learned dimensional analysis, you have been working at a fast food restaraunt for the past 35 years wrapping hamburgers. Each hour you wrap 184 hamburgers. You work 8 hours per day. You work 5 days per week. You get paid every 2 weeks with a salary of $840.34. How many hamburgers will you have to wrap to make your first one million dollars?
I just need some explanation on where to start or what I'm doing wrong, here's how I started.

step 1. 1hour/184 hamburgers
step 2. 1 day/8 hours
step 3. 1 week/5 days
step 4. $840.34/2 weeks

That's how I started, but it comes out as a fraction and that isn't right. What am I doing wrong?

Answer 1

'Per' means 'divided by'. When you read '8 hours per day', write that as '8hr / day'.

As well as getting the dimensions (mass, length, time) correct, you can use the same principles to check that you have conversion factors in place for any change of units of the same dimension(s).

Applying these principles to the calculation in the question gives:

(184 hamburger / hr)
* (8 hr / day)
* (5 day / wk)
* (52 wk / yr)
= (184 * 8 * 5 * 52) hamburger / yr.

(840.34 dollar / 2 wk)
* (52 wk / yr)
= (840.34 * 52 / 2) dollar / yr.

The hamburger to dollar ratio is:
(184 * 8 * 5 * 52) / (840.34 * 52 / 2) hamburger / dollar

The number of hamburgers needed to make 1,000,000 dollar is:
1,000,000 dollar
* [ (184 * 8 * 5 * 52) / (840.34 * 52 / 2)] hamburger / dollar
= 17516719.4 hamburger
Call it 17,516,720 hamburgers to be sure.