wailingkoh said:
Hi all
I need help
In the classes 6A and 6B, the total number of girls was 100% more than the total number of boys. The ratio of boys to girls in class 6A was 3 : 4 and the ratio of the boys to girls in class 6B was 1 : 6. If there were 8 more girls in class 6A than class 6B, find the number of pupils in class 6A.
Tks :)
Let $B_A$ be the number of boys in class 6A, $G_A$ be the number of girls in class 6A, $B_B$ be the number of boys in class 6B, and $G_B$ be the number of girls in class 6B.
Given that "the total number of girls was 100% more than the total number of boys," we may write:
$$2\left(B_A+B_B\right)=G_A+G_B$$
Given that "The ratio of boys to girls in class 6A was 3 : 4," we may also write:
$$4B_A=3G_A$$
Given that "the ratio of the boys to girls in class 6B was 1 : 6," we may also write:
$$6B_B=G_B$$
And given that "there were 8 more girls in class 6A than class 6B," we may also write:
$$G_A=G_B+8$$
Let's begin with the first equation:
$$2\left(B_A+B_B\right)=G_A+G_B$$
The 4th equation implies $$G_B=G_A-8$$ and so we now have:
$$2\left(B_A+B_B\right)=G_A+G_A-8$$
$$2\left(B_A+B_B\right)=2G_A-8$$
$$B_A+B_B=G_A-4$$
Using the 3rd and 4th equations, we find:
$$B_B=\frac{G_B}{6}=\frac{G_A-8}{6}$$
And so we now have:
$$B_A+\frac{G_A-8}{6}=G_A-4$$
$$6B_A+G_A-8=6G_A-24$$
$$6B_A+16=5G_A$$
Using the 2nd equation, there results:
$$3G_A+2B_A+16=5G_A$$
$$B_A+8=G_A$$
$$7B_A+56=7G_A$$
$$3B_A+3G_A+56=4B_A+4GA$$
$$B_A+G_A=56$$
Thus, we conclude there are 56 pupils in class 6A.