What is Mr Smith average wage per day?

Question

Mr Smith works for car factory for 3 days . For the first day ,he earns $120 and every following day he earns one and a half of his previous day.What is Mr Smith average wage per day?

Answer 1

120 + (120 + 60) + (180 + 90) / 3

570 / 3

190

 

His average daily salary is $190.

Answer 2

The problem essentially looks like this:

120 * 1.5 * 1.5 * 1.5....

because each day multiplies the money earned on the previous by one and a half, or 1.5.

Since we have a number that's repeatedly multiplying itself, we can use an exponent:

120 * 1.5^d

where d = the days worked.

However, since we have one day without the multiplier, we need to subtract that from the exponential:

120 * 1.5^d-1

1 - 1 = 0, and anything to the exponential power of 0 equals 1.

 

Day 1: 120 * 1 = 120

Day 2: 120 * 1.5 = 180

Day 3: 180 * 1.5 = 270

 

Comparison:

120 * 1.5² → 120 * 2.25 = 270