1950 AMC 12 Problem 30

Question

From a group of boys and girls,

15

girls leave. There are then left two boys for each girl. After this

45

boys leave. There are then

5

girls for each boy. The number of girls in the beginning was:

40

43

29

50

None of these

Let

G

and

B

be the original numbers of girls and boys

Translate the two ratios as

B=2(G-15)

and

G-15=5(B-45)

Let the original counts be

G

girls and

B

boys. The two conditions give

\begin{aligned} B&=2(G-15),\\ G-15&=5(B-45). \end{aligned}

Substituting the first into the second yields

\begin{aligned} G-15 &=5\bigl(2(G-15)-45\bigr)\\ &=10G-375. \end{aligned}

Hence

9G=360,

so

G=40.

Thus, the correct answer is A.

Problem 30 in other years