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When I say allowance, I mean like the kind you earned as a child. Here is the problem I am trying to solve. A parent has $20 they want to give to the child for doing all of their chores. If the child does all of their chores, they get 100% of their allowance. However is thy only do some of their chores they only get a percentage of their allowance. Here is my kicker. Not all chores are weighed the same.
The chores are weighted:

  • Big chores = 10
  • Medium chores = 5
  • Small chores = 1

If the parent setups a set of chores for the week:

  • 2 big chores(paint house, change oil)
  • 4 medium chores(clean room)
  • 7 small chores(brush teeth, wash dishes)

At the end of the week, the child only does:

  • 1 big chores(paint house)
  • 2 medium chores(clean room)
  • 3 small chores(brush teeth)

I am unsure how to calculate how much allowance the child gets and what the distributions per-chore would be for the $20. Could someone point me in the right directions? The reason I have this question is because I am building an IOS app to help parents and children manage household duties. Please forgive me if I tagged this question wrong, as I am not sure what tag this falls under.

Gerry Myerson
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Nathan Clark
  • 113

1 Answers1

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Total the number of points the parent assigns for the week; in this case, $47$: twenty for big chores, twenty for medium chores, and seven for small chores.

Compute the number of points the child achieved. In this case, $23$: ten for the big chore, ten for the two medium chores, and three for the small chores.

Since he accomplished $\frac{23}{47}$ths of the points, he should get $\frac{23}{47}$ths of the original offer: $$\left(\frac{23}{47}\right)\times \$20 \approx \$9.79.$$

Note that this matches reasonably well: the child did only a little under half the assigned chores, so he's getting only a little under half the money.

In general, total the number of points achieved, divide by the total number of points assigned, and multiply by the reward offered: $$\left(\frac{\text{points accomplished by child}}{\text{points originally assigned by parent}}\right)\times\left(\text{full allowance amount}\right) = \text{allowance earned.}$$ With this formula, if the child were to do more than was assigned, he would get a comparative "bonus" as well. If you want to prevent bonuses, then you should replace the computation on the left with the minimum between that computation and the full allowance amount.

Arturo Magidin
  • 398,050