Systems of Equations in Applications - College Algebra

Two investment accounts earn different annual interest rates. Account A earns 4% annually and Account B earns 6% annually. An investor places a total of $25000 in these accounts and earns $1180 in interest after one year. If the investor wants to redistribute the funds to earn exactly $1300 in interest next year while keeping the same total investment, how much additional money needs to be moved from Account A to Account B?
Answer: $6000 needs to be moved from A to B First, find the current distribution. Let $x$ = amount in Account A, $y$ = amount in Account B. We have $x + y = 25000$ and $0.04x + 0.06y = 1180$ . From the first equation, $y = 25000 - x$ . Substituting: $0.04x + 0.06(25000-x) = 1180$ , so $0.04x + 1500 - 0.06x = 1180$ , giving $-0.02x = -320$ , so $x = 16000$ and $y = 9000$ . For the new target of $1300, let $x'$ and $y'$ be the new amounts. We need $x' + y' = 25000$ and $0.04x' + 0.06y' = 1300$ . Solving: $y' = 25000 - x'$ and $0.04x' + 0.06(25000-x') = 1300$ , so $0.04x' + 1500 - 0.06x' = 1300$ , giving $-0.02x' = -200$ , so $x' = 10000$ and $y' = 15000$ . The change is from $16000 to $10000 in Account A, so $6000 moves from A to B.