Average daily pay with more jobs

Question

I have the following doubt:

I have two jobs, the first one I work for 20 days in a year and earn a total of 100 \$. The second one I work for 50 days and get 2,000\$. Therefore the average pay per day is therefore 2,100\$/70 days = 30\$/day.

If I worked both jobs the whole year I'd earn: $$ 100\$/20\text{ days}=5\$/\text{ day}$*$365=1,825\$/\text{year}$$

for the first job and

$$2,000\$/50 \text{ days}=40\$/\text{day}*365=14,600\$/\text{year}$$

for the second one. The average pay per day is therefore (1,825\$ + 14,600\$)/365days = 45\$/day. Which is the correct average per day?

Thank you

Answer 1

The correct average is the second one (but there are some typos). In fact, the average is a value which, substituted in the original values you need to average, gives the same earn.

thus

$$m\times 365+ m\times 365=\underbrace{1825+14600}_{\text{Total Annual Earn}}$$

that is

$$m=\frac{1825+14600}{365\times2}=22.5$$

you said that the first job gets 100\$ total for 20 days, that is $100/20\times365=1825$ per year and not 730 as you wrote

this question is similar to one of your previous ones

Answer 2

It depends on what you want to average. The first one is meaningful (how much an average worked day was paid ?). The second one is less (how much would you earn in average having both works ?).

Beside, there are few mistakes :

• you should divide $100/20 = 5$ (instead of $100/50 = 2$).

• $(730 + 14600)/365 = 42$, which is logical since you multiplied every term of your sum by $365$ just to divide by it right after summing. So you just ended up summing terms.

• I suppose you wanted to divide by the number of jobs, but then the number you get is meaningless to me (average pay if you work half first job, half the other ?).

Also be more careful about parenthesis and priorities.