Question 1205484
Ethan invested $19,000 for 1 year, part at 11% simple interest and part at 13% simple interest. If he earned a total of $2,290 in interest, how much was invested at each rate?
let the amount invested at 11% a be  x

 and the amount invested at 13% awill be 19,000 -x
−

 The formula for simple interest is  I=prt

The interest earned from the amount invested at 11% 
​
is given by  x*0.11*1 = 0.11x

 the amount invested at 13% =19000-x
interest earned  is given by 
(19,000−x)*0.13*1

2470-0.13x

total interest =2290

0.11x+2470+0.13x = 2290

-0.02x = 2290-2470

-0.02x =-180

x = 9000
19000-x =10000

Ethan invested $9,000 at 11% and $10,000 (since $ at 13%.