Two persons A and B have a total sum of $320. First, A gives 20% of what he has to B. Then B gives 20% of what he now has back to A . If the ratio of the final amount of person B to the final amount of person A is 1.5, what was the initial amount that person A had?
Let the initial amount of A = A
Let the initial amount of B = B
A + B = 320
A =320 - B
B =320 - A
A =[320 - B] - 0.20[320 - B]
B =[320 - A] +0.20[320 - B]
B =[320 - A] + 0.20[320 - B] - 0.20 {[320 - A] + 0.20[320 - B]} = -0.8 (A + 0.2 B - 384.)
A =[320 - B] - 0.20[320 - B] + 0.20 {[320 - A] + 0.20[320 - B]} = 0.04 (-5 A - 21 B + 8320)
A = 100 dollars - A started with
B = 220 dollars - B started with
