Let x be the amount he invest in the 6% account.
We know that he invested 3 times more in the 10% account, then he invested 3x in that account.
We know that in total he invested $3100, then he invested:
[tex]3100-x-3x=3100-4x[/tex]in the 8% account.
Now, the simple interest formula is given as:
[tex]A=Prt[/tex]where A is the interest generated in the year, P is the principal, r is the interest rate (in decimal form) and t is the time.
We know that the total interest in a year (that is t=1) is $268, then we apply the formula for each principal and each rate, and equate it to $268, that is:
[tex]0.06x+0.1(3x)+0.08(3100-4x)=268[/tex]Solving for x we have:
[tex]\begin{gathered} 0.06x+0.1(3x)+0.08(3100-4x)=268 \\ \text{0}.06x+0.3x+248-0.32x=268 \\ 0.04x=268-248 \\ 0.04x=20 \\ x=\frac{20}{0.04} \\ x=500 \end{gathered}[/tex]Once we know the value of x we can find how much he invested in each account:
He invested $500 in the 6% account.
He invested $1100 in the 8% account.
He invested $1500 in the 10% account.
