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

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Answer:

Choice C
Level of Difficulty E M H

You want to start this problem with some simple Let Statements, and the problem practically solves itself from there.

Let B = the original number of boys on the bus
Let G = the original number of girls on the bus

We are told that when the bus departs there are equal numbers of girls and boys, therefore B = G. At the first stop, 4 boys get off, so the number of boys is now B - 4. The number of girls remains G. We are then told that after the first stop, there are twice as many girls as boys. We set up a simple equation to represent this situation:

2(B-4) = G

This equation says simply that twice the number of boys that are on the bus after the first stop must equal the number of girls. You need to practice setting up equations like this until you are very comfortable with it.

Now, we have one equation and two unknowns (unsolvable because we have more unknowns than equations), so we will have to make a substitution to get rid of one unknown. Since B = G, we can replace the B with a G and write the new equation:

2(G-4) = G

Distribute the 2 to get:

2G - 8 = G

After subtracting G from both sides, we get:

G - 8 = 0

After adding 8 to both sides, we get:

G = 8, or choice C.

With practice, you will be able to do problems like this very easily.

For more practice with a wide variety of word problems, go to Skill Set 1: Word Problems.

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