Percentages / forming equation question

[spanishstar]

Hi just having a mind blank how to tackle and answer this question. Any help gratefully received:

In a barn there are just turkeys and geese. 60% of the birds in the barn are turkeys. The farmer sells 20 of these turkeys and after the sale the percentage of birds remaining in the barn that are turkeys is now 55%. By forming an equation work out how many geese are in the barn.

 

[Romsek]

start with T as the number of turkeys, G as the number of geese.
The number of birds is then N = T+G

T = 60% of N

then you sell 20 turkeys to get (T-20)
Now the number of birds is ?, call it N2
and (T-20) is 55% of N2

see what you can do now.

 

[Mr. Bland]

Using @Romsek's variable names, we have two expressions for the initial number of turkeys in terms of the initial number of birds:

[MATH]T = 0.6N[/MATH][MATH]T = 0.55(N - 20) + 20[/MATH]​

From here, we can solve for the initial number of birds. How might that be done?

 

[spanishstar]

Ok thanks so we could make 0.6N = 0.55 (N-20) + 20

So 0.6N = 0.55N - 11 + 20

So 0.05N = 9 so N =180


Hence there were 72 geese.

Quick question the '+ 20' in your T=0.55(N−20)+20 is that because we've taken 20 birds away so we need to get it back to the original number?

Thanks again

 

[Steven G]

Yes. The lhs of the equation is T so the rhs must also equal T (but probably will look different than T). Since the rhs w/o the + 20 will be 20 less than T (the lhs) we must add 20 to the rhs so it legitimately equals T

 

[Romsek]

I think a clearer solution is

\(\displaystyle
T + G = N\\
0.6 N + G = N\\
G=0.4N\\~\\

(T-20) = 0.55(N-20)\\
0.6N-20 = 0.55N - 11\\
0.05N = 9\\
N = 180\\
G = 0.4N = 72
\)

 

[spanishstar]

Thank you for all of your help and guidance.