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This problem is an application of a real life situation.
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The concept that will be involved in solving this problem is solving a system of linear equations.
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This particular system will involve three linear equations and three variables.
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In solving any type of application problem, one of the first things that you should do is state what your unknowns are knowns of.
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Are, what your variables are, and what each one represents.
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So with this problem, my unknowns involve amount of money invested in various types of accounts.
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So what i'm going to do is i'm going to let x be the amount of money that's invested, whoops, money invested in mutual funds.
01:13
I will let y be, why will represent the money, invested in government bonds and then i will say z is going to represent the money invested or not invested so much as let me say this money that was just put in a savings account okay so z is standard for the money put in a savings account now each of these different investments will pay a different rate of interest per year.
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So to help organize this information, i'm going to make a little chart.
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With this chart, i'm going to have a column for the type of investment, a column for the amount of money invested in that, the type for the rate of return as a decimal, and then the last column is going to be the interest or the return paid on the investment okay so we have mutual funds and that was x dollars and the mutual funds paid 3 % interest i'm sorry 2 % interest so that's a 0 .02 so the return on that we find by multiplying the rate times the amount of money so that's going to be a 0 .0x okay then we have our government bonds which is y dollars at 2 .5%, so i mean like that is a .025, and the rate will be a .025y.
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Then we have the savings account that we'll put money in, which is z dollars at 1 .25%, so that's 0 .125.
03:57
So the return is 0 .025 times c.
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Alright now with all the information in the problem with this chart we should be able to write our three equations.
04:14
Since $40 ,000 was invested, that first equation is going to be the amount placed in each of the different accounts added together to give us the $40 ,000.
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So there's our first equation.
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Then the second equation, we're going to use the idea that the amount invested in government bonds was twice the amount invested in mutual funds.
04:46
So the amount invested in government bonds is why, and that's twice the amount invested in mutual funds.
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Now i'm going to take this equation and manipulate it a little bit since it will make it easier to work with with the elimination method that we were using solving this system.
05:06
So if i subtract y from each side, i will have this equation.
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Okay, then the third equation is going to involve the interest that was earned.
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And that's why i organize the information into this table.
05:22
I know that the interest, the return from each of the three accounts, must total up to, must add up to, $825.
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So my next equation is going to be .02x plus 0 .025y plus 0 .0125c is the $825 that was earned in returns.
05:57
Now this equation, this third equation, i want to do something with.
06:03
If at all possible to eliminate decimals, it suggested that you do so.
06:10
Since the most number of decimal places is 4 in this problem, i'm going to multiply every term by 10 raise to the 4, which is the same thing as multiplying every term by 10 ,000.
06:28
Okay, so every term is going to be multiplied by 10 ,000 to produce an equivalent equation that does not have decimals.
06:40
Okay, so when i take the 0 .02 times the 10 ,000, i will get 200x, and then i will get 250y.
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I will have a hundred and twenty five z and that will equal 825 followed by four zeros.
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8 ,250 ,000.
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Now i have three equations for my system.
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This is the first equation.
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I will work with this as my second equation and then this i will take as my third equation.
07:31
When you solve in a system by elimination that contains three variables, one of the easy tasks to do is to take a pair of equations and try to eliminate a variable from that pair, and then take another pair and try to eliminate the same variable...