Question

During the summer, Joshua plans to work on his uncle’s soybean farm. His uncle says that Joshua has two options for being paid. For the first option, Joshua earns $20 each day he works. For the second option, he earns one nickel for agreeing to work, and that amount doubles each day he works after that. Joshua plans on working 3 days a week for 8 weeks. Which option should he choose?

Answer 1

The second option is best to choose.

Explanation:

Joshua plans on working 3 days a week for 8 weeks. Therefore, Joshua will work for (8 × 3) = 24 days.

For the first option, Joshua earns $20 each day he works. So, in 24 days he will earn (20 × 24) = $480.

For the second option, he earns one nickel for agreeing to work, and that amount doubles each day he works after that.

So, the total earning of Joshua after 24 days of work will be

0.05 + 0.1 + 0.2 + 0.4 + 0.8 + 1.6 + ......... up to 24 terms {Since 1 nickel is equal to $0.05}

Now, this is an G.P. series sum and first term is 0.05, common ration is 2 and the number of terms is 24.

So, the sum =
`0.05 * (2^(24) - 1 )/(2 - 1)`

= $838860.75

Therefore, the second option is best to choose. (Answer)