First, you know the average total:

T_avg = $10.30/(x+y)

where “x” is the number of girls and “y” the number of boys.

You also know that the total cost,

T= T_g*x + T_b*y, where T_g and T_b are the average spent by the girls and boys, respectively.

Therefore,

T_avg = T_g + T+b = T/(x+y)

or

$10.30*(x+y) = $9.70*x + $11.70*y

You have two unknowns and one equation. By definition, you cannot solve this mathematically.

Logically, however, you know that there has to be a whole number of boys and girls (x and y must be whole numbers, you can’t have 0.7598121 boys or something like this). Also, clearly both x and y must be positive.

So knowing x and y are both positive integers, you can plug and chug until you have the only solution where two whole numbers fit the equation. However, there may be more than one set of whole numbers for x and y that satisfy the equation.

You can do the plug and chug, it will get you the right answer eventually (set up an excel spread sheet – that’s the easiest).

UPDATE – ok, I set up the spreadsheet and got 4 girls and 3 boy. It checks out. You could also have any multiple of this: 8 girls and 6 boys, 12 girls and 9 boys, etc.

Similarly, let b be the number of boys, then

9.70*g + 11.10*b = 10.30

another equation is needed, the number of people in the sample must be known

I think that is how you would do it….but I’m not sure!

You need to substitute different numbers for g and b until it equals 10.3.

Idiot.

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