SAT 1 Math Question - Help on interpretation

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1

Ok… This is the whole question

There is the same number of boys and girls on a school bus when it departs from school. At the first stop, 4 boys get off the bus and nobody gets on. After the first stop, there are twice as many girls as boys on the bus. How many girls are on the bus
a. 4
b. 6
c. 8
d. 12
e. 16

The answer is 8.

I do know how to set up the equation and solve the problem. Putting x as boys and y as girls the equation would be:
x = y (since is the same number of boys and girls on a school bus when it departs)

Then I face a problem!

I set up equation as x-4 = 2y, but to get the right answer, I would need to put 2(x-4) = y.

It seems to me that I am interpreting this part of the problem --> “there are twice as many girls as boys on the bus” wrong. I would set up equation as x = 2y because for every boy there are 2 girls. Can someone point out the flaw for x = 2y?

And more I think about it I get confused. Please math gurus, help me!

2

x-4 = 2y is saying that the number of boys is twice the number of girls – the opposite of what you meant!

But in any case, this problem (like many on the SAT) is much easier if you skip the algebra and just play with numbers. And in this case, the answers are right there. Just pick one and play with it.

For example, if the answer was 6 girls, then there would have to now be 3 boys (half of 6). But that can’t be it because then before the 4 boys got off, there would have been 7 boys which is not the same as the 6 girls.

So you try another: could there be 8 girls? There would have to be 4 boys (half of 8). And then, before the 4 boys got off, there were 8 boys as well.

3

I set up 2 equations:

  1. b=g (b for boys, g for girls)
  2. 2(b-4)=g because after 4 boys leave, the number of girls = 2 times number of boys
    Now substitute and you get 2(g-4) = g and it’s simple to solve for g and get g=8.
4

For every boy there are two girls, or b/g = 1/2. Cross multiply and you get 2b=g.