Question 1199224
Let the amount of money invested into the first fund be {{{x}}}, and the amount of money invested into the second fund be {{{y}}}. Since we know that $500,000 was invested in total, we know that {{{x+y=500000}}}. In addition, since we know how much each fund makes, we also know that {{{0.052x+0.077y=34000}}}.
We have the system of equations {{{system(x+y=500000,0.052x+0.077y=34000)}}}. To get rid of the decimals, we multiply both sides of the second equation by {{{1000}}} to get {{{system(x+y=500000,52x+77y=34000000)}}}. Multiplying both sides of the first equation by 77, we get {{{system(77x+77y=38500000,52x+77y=34000000)}}}. Subtracting the second equation from the first, we get {{{25x=4500000}}}. Dividing both sides by {{{25}}}, we get {{{x=highlight(180000)}}}. Since we know that $500,000 was invested in total, we have {{{y=500000-180000=highlight(320000)}}}. Therefore, $180,000 was invested into the first fund, and $320,000 was invested into the second fund.