Respuesta :
Take into account the following formula for the simple interest:
[tex]I=P\cdot r\cdot t[/tex]where:
P: principal investment
r: interest rate
t: time
In order to determine the investments for both accounts, proceed as follow:
-Consider that both investments are represented by P1 and P2 respectively, then, you have:
[tex]\begin{gathered} P_1+P_2=22000 \\ P_2=22000-P_1 \end{gathered}[/tex]- Next, use the given values for parameters r and t for each investment:
8% = 0.08
11% = 0.11
t = 1 year
[tex]\begin{gathered} I_1=P_1\cdot0.08\cdot1=0.08P_1 \\ I_2=P_2\cdot0.11\cdot1=0.11P_2 \end{gathered}[/tex]- Next, consider that the sum of the total earnings is $1910, then:
[tex]I_1+I_2=1910[/tex]- Replace I1 and I2 by the expressions in terms of P1 and P2 and write down the resultant expression in terms of P1, as follow:
[tex]\begin{gathered} 0.08P_1+0.11P_2=1910 \\ 0.08P_1+0.11(22000-P_1)=1910 \\ 0.08P_1+2420-0.11P_1=1910 \\ -0.03P_1=-510 \\ P_1=\frac{510}{0.03}=17000 \end{gathered}[/tex]And for P2:
[tex]\begin{gathered} P_2=22000-P_1 \\ P_2=22000-17000=5000 \end{gathered}[/tex]Hence, the amount of money invested in each account was $5000 and $17000
