Alexius invests $24,500 in two accounts paying. 5% and 7% annual interest. How much was invested in each account if, after one year, the total interest was $1,595

He invested $6,000 in the account paying 5% and $18,500 in the account paying 7%Step-by-step explanation:The formula of the interest is I = Prt, whereP is the money invested r is the rate of interest in decimalt is the time of investmentAlexis invests $24,500 in two accounts paying 5% and 7% annual interest. After one year, the total interest was $1,595Assume that he invested $ [tex]P_{1}[/tex] in the account paying 5% annual interest and $ [tex]P_{2}[/tex] in the account paying 7% annual interest∵ The investment in the account paying 5% is $ [tex]P_{1}[/tex]∵ The investment in the account paying 7% is $ [tex]P_{2}[/tex]∵ He invests $24,500 in both accounts∴ [tex]P_{1}[/tex] + [tex]P_{2}[/tex] = 24,500 ⇒ (1)∵ [tex]I_{1}[/tex] = [tex]P_{1}[/tex] [tex]r_{1}[/tex] t∵ [tex]r_{1}[/tex] = 5% = (5/100) = 0.05∵ t = 1∴ [tex]I_{1}[/tex] = [tex]P_{1}[/tex] (0.05)(1)∴ [tex]I_{1}[/tex] = 0.05 [tex]P_{1}[/tex]∵ [tex]I_{2}[/tex] = [tex]P_{2}[/tex] [tex]r_{2}[/tex] t∵ [tex]r_{2}[/tex] = 7% = (7/100) = 0.07∵ t = 1∴ [tex]I_{2}[/tex] = [tex]P_{2}[/tex] (0.07)(1)∴ [tex]I_{2}[/tex] = 0.07 [tex]P_{2}[/tex]∵ The total interest is $1,595∴  [tex]I_{1}[/tex] + [tex]I_{2}[/tex] = 1,595 - Substitute the value of [tex]I_{1}[/tex] and [tex]I_{2}[/tex] in the equation∴ 0.05 [tex]P_{1}[/tex]  + 0.07 [tex]P_{2}[/tex] = 1,595 ⇒ (2)Now let us solve the system of the equationsMultiply equation (1) by -0.07 to eliminate [tex]P_{2}[/tex]∴ - 0.07 [tex]P_{1}[/tex] - 0.07 [tex]P_{2}[/tex] = - 1715 ⇒ (3)- Add equations (2) and (3)∴ - 0.02 [tex]P_{1}[/tex] = - 120- Divide both sides by - 0.02∴ [tex]P_{1}[/tex] = 6000∴ He invested $6,000 in the account paying 5%Substitute the value of [tex]P_{1}[/tex] in equation (1) to find [tex]P_{2}[/tex]∵ 6000 + [tex]P_{2}[/tex] = 24,500- Subtract 6000 from both sides∴ [tex]P_{2}[/tex] = 18500∴ He invested $18,500 in the account paying 7%He invested $6,000 in the account paying 5% and $18,500 in the account paying 7%Learn more:You can learn more about interest in brainly.com/question/10672611#LearnwithBrainly