Of a group of boys and girls at camp, 22 girls leave early for a trip to the amazon. In the remaining group, there are twice as many boys as girls. But then 40 boys leave on a whitewater rafting trip, and this leaves us with three times as many girls as boys. How many boys and girls were there in the original group?

Relevance

Let b = number of boys and g = number of girls initially.

If 22 girls leave, there are g - 22 left, and the problem says that b is twice as many. So we have

b = 2(g - 22)

Then 40 boys leave, giving b - 40 remaining. Now there are three times as many girls remaining, or

3(b - 40) = g - 22

Substituting for b in the second equation using the first, we get

3(2(g-22) - 40) = g-22 or after multiplyting and simplifying the left side

6g - 252 = g - 22 which is easily solved as g = 46

Then, subsitute 46 in the first equation for g, giving

2 (46 - 22 ) = b or b = 48.

As a reality check, walk through the problem and see if it works out.

• b = 2(g - 22), eq#1

3(b - 40) = g - 22, eq#2

multiply eq#2 by 2

2*3(b - 40) = 2*(g - 22)

6b - 240 = 2(g - 22)

subtract eq#1

5b - 240 = 0

b = 240/5

b = 48

g = b/2 + 22

g = 48/2 + 22

g = 46

• okay, let b be number of boys and

g be number of girls in original group,

then

b=2(g-22) and

3(b-40)=g-22.

SO, solving, you get

b=48 and

g=46.