According to the question, Greg had $30,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $2790 in interest. Then we write the following equations:
First account (10%): 0.1 x = a (money gained in one year, where x is the amount invested)
Second account (7%) : 0.07 (30.000 - x) = b (money gained in one year, where 30.000 - x is the amount invested inthe seond account).
a + b = 2790 (total amount of money gained due to interest).
Replacing the two first equations in the third one, we obtain the following expression:
0.1 x + 0.07 (30.000 - x) = 2790
(0.1 - 0.07)x + 2100 = 2790
0.03 x = 690, solving for x:
x = $23.000 (the amount of money invested in the first account) and
($30.000 - x) = $7.000 is the amount of money invested in the second account.