SOLUTION: Tina's diner is open six days a week. her income for the first five days this week was $200, $140, $360, $400, and $280. How much must she make on the sixth day to have a mean inco

Question 105701: Tina's diner is open six days a week. her income for the first five days this week was $200, $140, $360, $400, and $280. How much must she make on the sixth day to have a mean income of $390 for the six days?
Answer by fmo(8) (Show Source): You can put this solution on YOUR website!
Tina wants to realize a mean income of $390 in her six days of operation. The total amount of income she'll make, divided by the six days of work will give us this mean. I.e.,
weekly income / days worked = daily mean
We know that Tina will have worked six days when the week is over, so:
weekly income / 6 = daily mean
And we know that she's hoping to realize a mean of $390, so:
weekly income / 6 = $390
Now to make things look a little more like an equation we'll let x represent the weekly income.
x / 6 = 390
Solving for x we multiply both sides of the equation by 6 and get:
x = 2340
Again, x was how much Tina would have to earn over the six day work week, not how much she needed to make on the sixth day.
We know how much she made during the first five days; let's add them:
200 + 140 + 360 + 400 + 280 = 1380
So if Tina needs to make $2,340 in six days, and she's already made $1,380 in the first five, the difference between the two will be what she needs to make on the sixth day. I.e., letting i represent the income needed on day six:
i = 2340 - 1380
i = 960
Tina needs to earn $960 on her sixth day of work to have a mean income of $390 for the six days.

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