Question

two high school students are hired to rake leaves. They will work a couple hours each afternoon until the job is completed. They can choose one of the two payment plans. Plan A pays $11.50 per afternoon, while Plan B pays 2 cents for one day of work, 4 cents total for two days of work, 8 cents for three days of work, 16 cents total for four days, and so on. Each student chooses a different plan. On which day would their total pay be approximately the same?

Answer 1

On 14th afternoon their total pay will be approximately the same.

Explanation:

Let x be day on which both students will have their total pay approximately the same.

On xth day student who has chosen plan A will get $11.50x 0r 1150x cents, while student who has chosen plan B will get
`2^(x) \text{ cents}`.

Now we will equate both equations to solve for x,

`1150x=2^(x)`

Upon solving this equation by calculator we get
`x\approx13.9719`. Therefore, on 14th day both students will have their total pay approximately the same.