This problem is asking you to find 2 amounts or 2 variables. We'll call them P(Principle is 1st account) and P'(Principle in 2nd account). So you are going to have to use two equations, also called a system of equation.
Since this is a simple interest problem we should use the following formulas:
Interest = Principle*rate*time. or I = Prt
Amount(ending) = Principle + Interest. or A = P + I. or A = P + Prt (since I = Prt) or. A = P(1+rt) (factor out P)
Juan's total investment is 22,500, so P + P' = 22,500. This gives you equation 1.
Now, the total interest accrued is 1,735, so 1,735 = I + I' (meaning the interest from the 1st account plus the interest from the 2nd account. So, 1,735 = Prt + P' r' t', and since we know the interest rates and the time, 1,735 = P(0.13)(1) +P'(0.06)(1). Simplified, 1,735 = P(0.13) + P'(0.06).This gives you equation 2.
System of equations:
(1) 22,500 = P + P'
(2) 1,735 = P(0.13) + P'(0.06)
The most efficient way to approach solving this system is by substitution. Solve for P in equation 1 and plug it into equation 2. Then solve equation 2 for P'. Once you know what P' is equal to, subtract it from 22,500 to find P.
