An investment adviser invested $14,000 in two accounts. One investment earned 4% annual simple interest, and the other investment earned 2.5% annual simple interest. The amount of interest earned for 1 year was $458. How much was invested in each account?
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To solve this problem, we can use a system of equations. Let's call the amount invested in the account earning 4% interest "x" and the amount invested in the account earning 2.5% interest "y".
Since the total amount invested is $14,000, we have the equation:
x + y = 14,000 ...(Equation 1)
The total interest earned after 1 year is $458, which can be calculated by multiplying the amount invested in each account by their respective interest rates:
0.04x + 0.025y = 458 ...(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve the system by substitution:
From Equation 1, we can isolate x by subtracting y from both sides:
x = 14,000 - y
Now, substitute this value of x into Equation 2:
0.04(14,000 - y) + 0.025y = 458
Simplify and solve for y:
560 - 0.04y + 0.025y = 458
0.015y = 458 - 560
0.015y = -102
y = -102 / 0.015
y = 6,800
Now substitute the value of y back into Equation 1 to find x:
x + 6,800 = 14,000
x = 14,000 - 6,800
x = 7,200
Therefore, $7,200 was invested in the account earning 4% interest, and $6,800 was invested in the account earning 2.5% interest.