Rick Arico invested $5000; part at a yearly rate of 7% and part at a yearly rate of 9%. The total interest earned for one year was $368. How much did he invest at each rate?

Rick Arico invested $4100 at a yearly rate of 7% and $900 at a yearly rate of 9%.

Step-by-step explanation:

Let x represent the amount invested at 7% yearly rate and let y represent the amount invested at 9%.

$5000 was split and invested at 7% yearly rate and 9% yeatly rate. Therefore:

x + y = 5000         (1)

For the 7% yearly rate:

Interest = (x * 7%) = 0.07x

For the 9% yearly rate:

Interest = (y * 9%)  = 0.09y

The total interest = interest for the 7% yearly rate + Interest for the 7% yearly rate = 0.07x + 0.09y

Given that the total interest earned in the year was $368, hence:

0.07x + 0.09y = 368      (2)

To find x and y, we have to solve equation 1 and equation 2 simultaneously. multiply equation 1 by 0.07 and subtract the result from equation 2 to get:

0.02y = 18

y = 18 / 0.02

y = $900

Substitute y = $900 in equation 2:

0.07x + 0.09(900) = 368

0.07x + 81 = 368

0.07x = 287

x = $4100

Therefore Rick Arico invested $4100 at a yearly rate of 7% and $900 at a yearly rate of 9%.