00:01
Okay, so i'm going to answer the student question with the inheritance of $40 ,000 divided among three accounts, having an interest of $3 ,500 a year.
00:10
The interest rate is $7, 9, and 11 for each account.
00:14
We have a little bit of information about account 9, or the interest rate on 9 % had $3 ,000 less than that of 7%.
00:22
We are going to come up with the equations for this system, and we are going to solve it to figure out the investment account in each place.
00:30
So i'm going to start it off by just creating some language for the accounts.
00:37
A9 is going to correspond to the 9 % interest account, a7, the 7 % interest account, and a11, the 11 % interest account.
00:50
Setting up the three equations, we know right off the bat that a9 plus a7 plus a11 is equal to $40 ,000.
01:05
And we know that the interest rates on each one correspond to 3 ,500, so we can say, we'll line them up.
01:14
0 .09 % times the amount in account 9 plus 0 .07 times the amount in account 7 plus 0 .11, plus 0 .11 times the amount in the 11 % account comes out to 3 ,500.
01:43
Clear yep okay and we are loving a little bit information here we know that a 9 is equal to a 7 minus 3 ,000 so this is part a right here this is your set of three equations given based on the problem all three accounts is $40 ,000 each account interest times the balance in each account comes out to $3 ,500 and account 7 has $3 ,000 in it more than a count nine does.
02:21
Now, in order to do part b and actually identify some values for this, the first thing you want to look at is we have a lot of stuff in terms of a7.
02:31
This one will give us a7 very quickly.
02:33
Replace all the a9s with a7s, and we can start to break this down into something we can solve.
02:39
So the first thing that i would do is plug this equation here, this a9 value, into this equation here, and that gets rid of a variable just off of that.
02:51
So copying that in, we have a7 minus 3 ,000 plus a7 plus a11 is equal to 40 ,000.
03:07
And then we can take equation 2 here and solve it for a11.
03:14
So a11 corresponds to the amount in account 11, just again.
03:19
And when you solve that, you get a little bit of fractional stuff.
03:23
But to prevent all that, i'm just going to leave everything in big terms.
03:26
If you use a calculator, you're going to end up with very small numbers like .636 repeating, 0 .818 and 3888 repeating, or 31818 repeating.
03:38
So to leave it all algebraically, you're going to have the 3 ,500, okay, and you are going to subtract off 0 .09 -09 minus 0 .07a7, and then you are going to divide the entire equation by 0 .09 .0 .07 .7.
03:57
And then you are going to divide the entire equation by 0 .0 .0 .7.
03:58
And now we're going to take that number for a11 which is in terms of a9 and a7 and plug it into this expression and then we take this expression right here let's get a different color and plug this into this spot for a9 so coming from that we get that a7 minus 3000 plus a7 plus this 3500 minus .09 times a7 minus 3 ,000.
04:45
And that's this brown line here.
04:47
I can extend that down.
04:51
It's the same thing...