He invested $6500 in bonds
Step-by-step explanation:
The formula of the simple interest is I = Prt, where
- P is the invested amount
- r is the rate of interest in decimal
- t is the time of investment
Assume that Mike invested $x in stocks and $y in bonds
∵ Mike invested $x in stocks
∵ Mike invested $y in bonds
∵ Mike invested a total of $25,000
∴ x + y = 25000 ⇒ (1)
∵ The interest rate of the stocks is 7%
∴ r of the stocks = 7 ÷ 100 = 0.07
∴ I (stocks) = x(0.07)(1)
∴ I (stocks) = 0.07x
∵ The interest rate of the bonds is 11%
∴ r of the bonds = 11 ÷ 100 = 0.11
∴ I (bonds) = y(0.11)(1)
∴ I (bonds) = 0.11y
∵ Mike earned $2010 interest on his investments
- Equate the sum of I (stocks) and I (bonds) by 2010
∴ 0.07x + 0.11y = 2010 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -0.11 to eliminate y
∵ -0.11x - 0.11y = -2750 ⇒ (3)
- Add equations (2) and (3)
∴ -0.04x = -740
- Divide both sides by -0.04
∴ x = 18500
- Substitute the value of x in equation (1) to find y
∵ 18500 + y = 25000
- Subtract 18500 from both sides
∴ y = 6500
∵ y represents the amount of money he invested in bonds
∴ He invested $6500 in bonds
He invested $6500 in bonds
Learn more:
You can learn more about the system of equations in brainly.com/question/6075514
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