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# Working with rate of interests

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Invest a total of \$4000 in 2 stocks that paid 5% and 7% annual interests. At the end of the year total interests from these investments is \$230. How much was invested at each rate?

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We will prepare two equations from the given data,

Let the amounts be x and y

they add up to 4000\$, that is x + y = 4000 ------(1)

We received a total of 230\$ as interest,
that is,

x * (5/100) + y * (7/100) = 230

Or, 5x + 7y = 23000 -----(2)

But we know, y = 4000-x

Substitute in 2,

5x + 7 * (4000-x) = 23000

or, 5x - 7x + 28000 = 23000

or, -2x = 23000 - 28000 = - 5000

or x = 2500

Now, y = 4000 - 2500 = 1500

Thus the amounts are 2500\$ and 1500\$

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