Problem

Explain the error in each statement. a. If 3 poun…

02:24

Problem 64 Hard Difficulty

Write an investment problem to fit the following equation, and
then solve it.
$$
0.08 x+0.07(10,000-x)=770
$$

Answer

$I_{1}=7000 \quad I_{2}=300$

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Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 6

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Video Transcript

problem. 64 reads for an investment problems if it the following equation and then solve it. So we have the equations airplanes, right, X plus 0.7 times 10,000 minus X is equal to 770. So I started off by writing off the equation and then making a chart, Um, for a first investment in a second investment and having the equation principal times right times. Time is equal to the interest. Um, so from the equation, we can see that the total interest earned is $770 so I'm going to fill that in. And so this first part of the equation has 0.0 X. So I'm going to say that that is our interest equation for our first company, which is gonna be a tech company. And then the second longer part of the equation 0.7 times 10,000 minus X is going to be the interest equation for the second company or the second investment. And so from here, I can see that the decimals in front of the equation or in front of the ex, is going to be our interest rates. So for this first company, it's gonna be 0.8% interest, which, as a percentage is 8% and then 0.7 is gonna be 7%. I can see that the first investment. We have an unknown amount that is being invested. And then the second investment. I see that $10,000 minus that first unknown amount, will represent the investment amount for that second investment. So now I know that $10,000 was the total amount that was invested. So having those out this information, I'm gonna assume that the time is just gonna be one. Um, I came up with an equation or a problem. Um, so the problem reads. A college student has $10,000. She wants to invest in the stock market. She invested two companies a tech company and an auto company, the tech company has, and 8% annual simple interest rate. While the auto company has a 7% annual simple interest rate. In the first day of her investment, she earned $770 in interest. How much did she invests in the tech company? So from here I am going to solve this equation, so I'm gonna rewrite it. 0.0 x plus 0.7 times 10,000 minus X is equal to 770. So I want to get rid of the decimals. So I'm going to multiply 100 on both sides of the equation. Some first gonna have to multiply 100 times their points through eight X and that is going to be eight eggs. And then I have 100 times their points or seven, which is just seven. And then I still have to multiply that by 10,000 minus X is equal to I have 770 times 1000 and that's gonna make 77,000. From here, I'm going to distribute the seven to the 10,000 as well as to the negative X. So now I have eight eggs plus seven times 10,000 is 70,000 and then seven times negative. X is negative. Seven X is equal to 77,000. Now I'm gonna combine the light terms. So I have eight x minus seven x and that makes one ex or just X. So I have X plus 70,000 is equal to 77,000 and then I want I say, the ex. I want to get along someone to do the inverse operation, since it's a one step equation and I'm going to subtract 70,000 on each side of the equation. So 70,000 minus 70,000 is zero. So that I'm left with X is equal to 77,000. Minus 70,000 is 7000. So x represents the amount invested in the tech company, so our solution is gonna be $7000 was invested in tech.

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