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Nimfa-mama [501]
3 years ago
13

An actor invests some money at 9​% simple​ interest, and ​$24,000 more than three times the amount at 10​% simple interest. The

total annual interest earned from the investment is ​$38,670. How much did he invest at each​ amount? Use the​ six-step method.
Mathematics
1 answer:
Andrew [12]3 years ago
8 0

Answer:

The amount invested at 9% is $93000

The amount invested at 10% is $303000

Step-by-step explanation:

Let the amount invested at 9% interest rate be x

And the amount invested at 10% rate be y

Simple Interest from x in a year = 0.09x

Simple Interest from y in a year = 0.1y

But y = 24000 + 3x

And the sun of the interests, 0.09x + 0.1y = 38670

Now we have a simultaneous eqn

y = 24000 + 3x (eqn 1)

0.09x + 0.1y = 38670 (eqn)

Substitute y into eqn 2

0.09x + 0.1(24000 + 3x) = 38670

0.09x + 2400 + 0.3x = 38670

0.39x = 38670 - 2400

x = 36270/0.39 = $93000

y = 24000 + 3x = 24000 + 3 × 93000 = $303000

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Step-by-step explanation:

We have the two functions:

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This is the same thing to f(144)-g(144).

So, let’s determine the value of f(144) and g(144) first:

\begin{aligned} f(144)&=\sqrt{144}+12 \\ &=12+12 \\ &=24\end{aligned}

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Since we know the hypotenuse and we know one of the legs, in order to find the second leg we just substitute the values and solve the equation and so we get...

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8.4/10

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