Grade 6 Math-Percentage homework help.... Thank you?

Total # of candies was 1806, boys got 294 more so 1806/2=903, 903-294=609, or the # the girls got, and 903+ that extra 294=1197,or the #the boys got... Obviously there's fewer boys here, because dividing the sweets evenly the girls got less each because of there being more of them... So find the largest # that can go into 1197 evenly, subtract 4, should be the max # that goes into 609 evenly, which should be the number of boys and girls... If I'm wrong then there's just a flaw in the math somewhere but you should be able to figure it out now...

Let
x = the number of girls
y = the number of boys

If 25% of the boys left the computer club, the ratio of the number of boys who remained to the number of girls would be 5:8.

(a)What was the ratio of the number of boys to the number of girls in the computer club?

25% = 25/100 = 1/4
So, if 1/4 of the boys left, there would remain 3/4. In mathematical terms the ratio would then be:

(3/4)y / x = 5/8.

But as actually nobody has left, the ratio is:

y / x = (5/8) / (3/4) = 5/6.
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[...] each girl received 4 sweets fewer than each boy. They received 294 more sweets than the girls and a total of 1806 sweets were given out.

And the ultimate question is:
(b) What was the total number of boys and girls in the club?

We'll firstly have to figure out how those sweets were distributed. And we introduce another unknown:

n = number of sweets for each girl.
xn = number of sweets for the girls (in total). And
y(n + 4) = sweets for the boys, as each boy gets 4 sweets more than each girl.

The ratio y:x = 5:6 is now very useful, because it follows immediately:

y = (5/6)x, and
x = (6/5)y, which comes in handy for substitution purposes.

Now we can build our system of two linear equations:
(Note that I have rephrased the 1st condition to: "Each boy gets 4 sweets more than each girl". If you want to do it according to the original text, n would then represent the number of sweets for each boy, and the number of sweets for the subset of girls would then equal x(n - 4).)

(1) y(n + 4) + nx = 1806

The boys received 294 more sweets than the girls, which is just the difference:

(2) y(n + 4) - nx = 294

Resolve parentheses and substitute (6/5)y for x

(1.1) ny + 4y + (6/5)ny = 1806
(2.1) ny + 4y - (6/5)ny = 294

(1.2) (11/5)ny + 4y = 1806
(2.2) -(1/5)ny + 4y = 294 ;; Times 11
(2.3) -(11/5)ny + 44y = 3234

Add equations (1.2) + (2.3)

48y = 5040
y = 105.

There are 105 boys in the club.

As x=(6/5)y, x = 126.

There are 126 girls in the club.

x + y = 231.

The total number of boys and girls in the club is 231.

Btw, each girl gets 6 sweets, and each boy gets 10.