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
- P is the money invested
- r is the rate of interest in decimal
- t is the time of investment
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 $ in the account paying 5% annual interest and $ in the account paying 7% annual interest
∵ The investment in the account paying 5% is $
∵ The investment in the account paying 7% is $
∵ He invests $24,500 in both accounts
∴ + = 24,500 ⇒ (1)
∵ = t
∵ = 5% = (5/100) = 0.05
∵ t = 1
∴ = (0.05)(1)
∴ = 0.05
∵ = t
∵ = 7% = (7/100) = 0.07
∵ t = 1
∴ = (0.07)(1)
∴ = 0.07
∵ The total interest is $1,595
∴ + = 1,595
- Substitute the value of and in the equation
∴ 0.05 + 0.07 = 1,595 ⇒ (2)
Now let us solve the system of the equations
Multiply equation (1) by -0.07 to eliminate
∴ - 0.07 - 0.07 = - 1715 ⇒ (3)
- Add equations (2) and (3)
∴ - 0.02 = - 120
- Divide both sides by - 0.02
∴ = 6000
∴ He invested $6,000 in the account paying 5%
Substitute the value of in equation (1) to find
∵ 6000 + = 24,500
- Subtract 6000 from both sides
∴ = 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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