00:01
Hi here in this question we are given that the amount is borrowed at 10 percentage 12 percentage and 14 percentage so let them be x y and z respectively so here the total amount that is is overro is equal to $39 ,000 and it is clear that the value of x plus 5 ,000 z is equal to $39 ,000.
00:37
So here the yearly interest is equal to $4 ,700.
00:54
So here our equation would be 0 .1x plus 0 .1 to y plus 0 .14 set is equal to 47 hundred dollars now here let this be our equation 1 this is our equation 2 and then further since the amount borrowed at 14 is double then amount borrowed at 10 and 12 together so here our new set of equation would be x plus y equals to 2x so here now let this be our third equation we can also reframe as x plus y minus 2 z equals to 0 let this be our equation 3 now here our equation 2 we can further simplify our equation 2 and can be rewritten as 50 multiplied with 0 0 .1 x plus 0 .125 plus 0 .14 z is equal to 50 multiplied with 40 ,700.
02:30
So here we have 5x plus 6y plus 7 z equals to 2 like 35 ,000.
02:42
Let this be our equation 4.
02:45
Now here using these four equations like equation 1, 3 and 3.
02:53
4 here we can write a system of equation and using them we can form an argument matrix so here our argumented matrix is 1 -11 -567 1 -1 -1 minus 2 and here 39 ,000 2 lakh 35 ,000 and 0 so now here we need to perform the various row operations and then we need to solve this even system of equations.
03:26
So here first of all we perform a row operation r2 minus 5 tenths of r1 in r2.
03:34
So here we have 1 -111 -0 -1 -1 -2.
03:41
Here we have 39 ,000, 40 ,000 and here is 0...