fraction word problem including word problem

Question

There were 490 children altogether in two groups. Group A only consists of boys and Group B only consists of girls. There are 2.5 times as many girls as boys. Some girls joined Group B and for every 4 boys in group A. 32 more boys joined the group. The total number of girls was then 1/3 the total number of boys. Express the number of girls who joined Group B as a fraction of the number of boys who joined Group A.

Answer 1

Let number of boys be B and the number of girls 490-B. These are also the sizes of the groups A and B. 490-B=2.5B means there are 2.5 times as many girls as boys. From this we can find B: 3.5B=490, so B=490/3.5=140 and the number of girls (group B) must be 490-140=350. Let the number of girls joining group B (the girls' group) be G. The number of boys joining group A is (140/4)*32=1120. Group A now contains 140+1120=1260 boys. Group B now contains 350+G=(1/3)*1260=420 and the number of girls joining group B becomes 420-350=70. So we can express G as a fraction of the number of boys joining group A: 70/1120=1/16(=G/8B=((1/3)(B+8B)-(490-B))/8B=(3B-490+B)/8B=(4B-490)/8B=(2B-245)/4B). The fraction is 1/16.