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, where
Alexis invests $24,500 in two accounts paying 5% and 7% annual
interest. After one year, the total interest was $1,595
Assume 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 equations
Multiply 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%
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