Mrs. martinez has $10,000 to invest.One bank offers her a return of 7.5% on the whole sum. Another bank offers her a return of 8% on part of the sum, and 6% on the rest of the sum. How much of the $10,000 would need to be invested at 8% at the second bank, for the overall to be the same as at the first bank?
we want to know when
.075*10000 = .08x + .06(10000-x)
x = 7500
.075*10000 = .08x + .06(10000-x)
x = 7500
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.075*10000 = .08*7500 + .06(10000-7500)
.075*10000 = 600 + .06(2500)
.075*10000 = 600 + 150
.075*10000 = 750
750$
To determine how much of the $10,000 should be invested at 8% at the second bank, we need to find the point where the overall returns from both banks are equal.
Let's assume that x dollars are invested at 8% at the second bank. This means the remaining amount, which is (10,000 - x) dollars, will be invested at 6%.
To find the overall return at the second bank, we can calculate the return from the 8% investment and the return from the 6% investment and add them together.
Return from the 8% investment = x * 8% = 0.08x
Return from the 6% investment = (10,000 - x) * 6% = 0.06(10,000 - x)
The overall return from the second bank is the sum of these two returns:
Overall return from the second bank = 0.08x + 0.06(10,000 - x)
Since we want the overall return to be the same as the first bank, which offers a return of 7.5%, we can set up an equation:
0.08x + 0.06(10,000 - x) = 7.5%
Now, we can solve this equation to find the value of x.