Problem

If the graph of $y=m x+b$ passes through quadrant…

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Problem 106 Hard Difficulty

Investments. Joni received $\$ 25,000$ as part of a settlement in a class action lawsuit. She invested some money at $10 \%$ and the rest at a $9 \%$ simple interest rate. If her total annual income from these two investments was $\$ 2,430,$ how much did she invest at each rate?

Answer

7000 at $9 \%$ and 18000 at $10 \%$ simple interest rate.

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Algebra

Elementary and Intermediate Algebra

Chapter 3

Graphing Linear Equations and Inequalities in Two Variables; Functions

Section 5

Slope–Intercept Form

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Video Transcript

So here's the situation where this person receives $25,000 she invested and she invest some of it at one interest rate and some of it at another interest rate. And so to find a variable way to explain that here's a new miracle. Example First. So let's say, for the 10% interest rate, she invests 10,000 of it. What does she invest at the 9% rate? Well, what's left over? It would be 15,000. And how did you get that? That was 25,000 minus 10,000. What was already used? What if she invested 1000 at the 10% rate? How much did she invest? At the 9% rate? That would be 24,000. How did you get that? 25,000. The total minus what was already used? 1000. So let's generalize. Suppose she invests X at the 10% rate. How much does she invest? At the 9% rate? It's whatever's left, which is 25,000 minus X. So that's an important part of the problem. So now what we want to do is make an equation that talks about the interest earned. So to get the interest earned, you multiply the amount invested by the interest rate. So in the 10% account she invests X, so the interest rate 100.1 multiplied by the amount invested X will give us her interest. And for the other account, her interest rate is 9%. So 90.9 multiplied by the amount invested. 25,000 minus X will give us her interest. Add those two amounts of interest together and we get her total interest, which is the income that they're talking about in the problem of 2430. And we'll solve this equation for X. So let's go ahead and distribute the 0.9 So we have 0.1 x plus. Let's see here 22 50 minus 0.0, Nynex equals 24 30. Oops. Okay, now let's go ahead and combine like terms. So we have 0.1 x and minus 0.9 x, and that gives us 0.1 x and let's subtract 22 50 from both sides. So when we do that, we get 1 80 Divide both sides by 0.1, and we get 18,000. So What does that mean? While X was the amount invested in the 10% account, So we know she invested, um, 18,000 in that one, and then what's left? What's left of 7000 because the total is 25,000 so 7000 was invested in the 9% account.

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