A few days ago
zlehc

a survey of random sample of people leaving an amusement park showed an average expenditure of \$10.3- for teh evening. The average expenditure for girls in the sample was \$9.70 and for the boys it was \$11.10. how many boys are there in the random sample?

A few days ago
ZenPenguin

Can’t solve this problem using mathematics. You can solve it using logic.

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.

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A few days ago
hero
Let g be the fraction of girls i.e. the number of girls divided by the total number of people in the sample

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

0

A few days ago
Pioneer
You do not have enough information to determine the number or percentage of boys since you are not given the total number in the random sample.
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A few days ago
johngalt4273
through logic, you know there are more boys than girls sampled, but you do not know the total number of people. This problem is unsolvable without that information. All you can determine is a ratio.
1

A few days ago
Anonymous
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A few days ago
Anonymous
(9.7g + 11.1b)/2 = 10.3

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.

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A few days ago
MathGoddess
Emily, if you’re too stupid to answer the question just move on and keep your moronic comments to yourself.

Idiot.

.

2

A few days ago
Anonymous