MHB Uncovering the Number of Pupils in Class 6A

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The discussion centers on calculating the number of pupils in class 6A based on given ratios and relationships between boys and girls in classes 6A and 6B. It establishes that the total number of girls is 100% more than the total number of boys, with specific ratios of boys to girls for each class. The calculations lead to the conclusion that there are 56 pupils in class 6A. The problem-solving process includes setting up equations based on the ratios and relationships provided. Ultimately, the solution is derived through algebraic manipulation of these equations.
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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 :)
 
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Hello wailingkoh! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far in your latest 2 threads?

Also, our "Other Topics" forum in the "Pre-University" forum group is meant for "Algebra-based Physics, Chemistry, Biology" questions. The questions you have been posting are best posted in our "Pre-Algebra and Algebra" forum, and so that's why I have been moving them.
 
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.
 
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