Answers (2)
You will have two equations.
Lets call number of girls=g and number of boys=b
You know there are 54 less boys than girls.
the number of boys=the number of girls minus 54
b=g - 54
You know there are 6% more girls than boys.
the number of girls=the number of boys plus 6%the number of boys
g=b+.06(b)
You are going to place the first equation into the second to find the number of girls.
g = (g - 54) + (.06 (g - 54) )
g = g - 54 + .06g - .06*54
subtract g from both sides and multiply .06*54
0=-54 + .06g - 3.24
add 54 to both sides and add 3.24 to both sides
57.24=.06g
divide by .06
g=954
The number of girls (g) is 954
We know that there are 54 less boys so the number of boys is 900.
To check your answer put the second equation into the first and you should come out with b=900 then add 54 to get the number of girls as 954.
Girls are 954
Boys are 900
You can also see that 954 is 6% more than 900
900 + .06(900)=954
I have a different approach than #xhriscomedy due to a different understanding of the problem:
There is a set of kids {K} = {k[1],k[2],k[3],...,k[m+n]} which consists exclusively and completely of the two exhaustively disjoint subsets {B} = {b[1],b[2],b[3],...,b[m]} and
{G} = {g[1],g[2],g[3],...,g[n]}, one of which consists of all the boys b while the other contains all the girls g. So, the number of kids amounts to 100%.
The percentage of boys b% plus the percentage of girls g% sums up to 100%:
b% + g% = 100%.
"The girls are 6% more than the boys":
b% + 6% = g%
Thus
2*b% + 6% = 100%
2*b% = 94%
b% = 47%
g% = 53%.
The 6% difference is given as 54 (less boys than girls). Hence
1% = 9
100% = 900
and calculating the actual numbers from the percentage ratio yields:
b = 900 * 0.47 = 423 boys and
g = 900 * 0.53 = 477 girls.