see question below?

Question

Jane invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. She received yearly interest of $130. Randy also invested in the same scheme, but he interchanged the amounts invested, and received $4 more as interest. How much amount did each of them invest at different rates?

Answer 1

let jane's investment in 12% rate be x
let jane's investment in 10% rate be y

as she recieves 130$ yearly: 0.1y + 0.12x = 130 #1
for Randy's case: 0.12y + 0.1x = 134 #2
#1*1.2 : 0.12y + 0.144x = 156 #3
#3-#2: 0.044x=22
x=500
in #1 0.1y+60=130
0.1y=70
y=700
So Jane had invested 500$ in 12% rate and 700$ in 10% rate
While Brandy had invested 700$ in 12% rate and 500$ in 10% rate