Answer :
Simple interest is represented by the following expression:
[tex]\begin{gathered} I=\text{Prt} \\ \text{where,} \\ I=\text{ interest} \\ P=\text{principal} \\ r=\text{interest rate in decimal form} \\ t=\text{ time (years)} \end{gathered}[/tex]We need to create a system of equations:
Let x be the money invested in the account that paid 6%
Let y be the money invested in the account that paid 10%
So, he received a total of $920 in interest, then:
[tex]920=0.06x+0.1y\text{ (1)}[/tex]And we know that money invested must add together $10,000:
[tex]x+y=10,000\text{ (2)}[/tex]Then, we can isolate y in equation (2):
[tex]y=10,000-x[/tex]Now, let's substitute y=10,000-x in the equation (1):
[tex]\begin{gathered} 920=0.06x+0.1(10,000-x) \\ 920=0.06x+1000-0.1x \\ 0.1x-0.06x=1,000-920 \\ 0.04x=80 \\ x=\frac{80}{0.04} \\ x=2,000 \end{gathered}[/tex]That means, he invested $2,000 in the account that paid 6% simple interest. Now, having x, we are going to substitute x in the second equation (2):
[tex]\begin{gathered} y=10,000-x \\ y=10,000-2,000 \\ y=8,000 \end{gathered}[/tex]He invested $8,000 in the account that paid 10% simple interest per year.