Allowance distribution problem 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.
 A: 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.
