Ratios & Solving for x.?

Question

I have the answers to these, I just need to work them out and

then check my answers but I don't understand it.

A) 3x + 2b = a

B) x + 2a = 3x - a

Ratios -

A) The ratio of girls to boys is 6:7. If there are 1,352 students enrolled in the school TODAY, how many girls and boys attended ?

Answer 1

A)

3x+2b=a

3x=-2b+a

x=-2/3b+1/3a

B)

x+2a=3x-a

x+3a=3x

3a=2x

1.5a=x

x=1.5a

Ratios

A)

6+7=13

1352/13=104

104x6= 624 girls

104x7= 728 boys

Answer 2

Solving for x means 'get x all by itself on the left side'.

A)

3x+2b=a

Subtract 2b from both sides

3x=a-2b

Divide both sides by 3

x=(a-2b)/3

B

x+2a=3x-a

Subtract 2a from both sides

x=3x-3a

Subtract 3x from both sides

-2x=-3a

Divide both sides by -2

x=(3a)/2

Let x be the number of girls.  Then 1352-x is the number of boys

6/7=x/(1352-x)

Cross multiply

6*(1352-x)=7x

8112-6x=7x

8112=13x

x=624

There are 624 girls and 728 boys.

_/

Answer 3

A) 3x + 2b = a

3x = a - 2b

x = (a - 2b) / 3

Or, if you don't like the way that looks

x = (1/3)a - (2/3)b

B) x + 2a = 3x - a

2a + a = 3x - x

3a = 2x

(3/2)a = x

Now, for ratios....

Set 6/7 equal to x/1352. Now what you need to do is solve for x, and you can accomplish this by cross-multiplication.

7x = 6 (1352)

7x = 8112

x = 1158.9

Hope that helps!