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?

Guest Oct 15, 2020

#1**0 **

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**

Guest Oct 15, 2020