x-money\ the\ money\ that\ the\ town\ invested\ in\ fund\ \# 1\\y-money\ the\ money\ that\ the\ town\ invested\ in\ fund\ \#2\\4\%=0.04;\ 6\%=0.06\\\\ \left\{\begin{array}{ccc}x+y=25,000&|muliply\ both\ sides\ by\ (-4)\\0.04x+0.06y=1,300&|multiply\ both\ sides\ by\ 100\end{array}\right\\\\+\left\{\begin{array}{ccc}-4x-4y=-100,000\\4x+6y=130,000\end{array}\right\ |add\ the\ sides\ of\ the\ equations\\------------\\ . 2 x = 30 , 000 ∣ d i v i d e b o t h s i d es b y 2 . x = 15 , 000 s u b t i t u t e v a l u e o f t h e x t o e q u a t i o n x + y = 25 , 000 15 , 000 + y = 25 , 000 ∣ s u b t r a c t 15 , 000 f ro m b o t h s s i d es x = 10 , 000 A n s w er : T h e t o w n in v es t e d $15 , 000 in f o u n d #1 an d $10 , 000 in f o u n d #2.
The town invested $10,000 in the fund with a 4% return and $15,000 in the fund with a 6% return. This was calculated by setting up two equations based on the total investment and total interest earned. By solving these equations step by step, we determined the amounts for each fund.
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