Delta inherited 25, 000 and invested part of it in a money...

Delta inherited $25, 000 and invested part of it in a money market account, part in municipal bonds, and part in a mutual fund. After one year, she received a total of $1, 620 in simple interest from the three investments. The money market paid 6% annually, the bonds paid 7% annually, and the mutual fund paid 8% annually. There was $6,000 more invested in the bonds than the mutual funds. Express the information in the form of system of equations.

Transcript

00:01 This is your question number 55 flat x is equal to the amount invested at 4 percent y is equal to the amount invested at 7 percent and z is equal to the amount invested at 8 percent so your total amount is 2 .5 million dollars so we can write x plus y plus that is equal to 2 .5 right now your total interest is 0 .178 million dollars so here is 0 .04x plus 0 .07y plus 0 .0 8 z is equal to 0 .178.

00:42 Now multiply 100 both side.

00:44 So here 4x plus 7y plus 8 z is equal to 17 .8.

00:56 Now your amount invested in government bond is 0 .3 million more than twice the amount invested in money market fund.

01:06 So we can write here.

01:07 X is equal to 2y plus 0 .3 so here negative 2y plus z is equal to 0 .3 this is our third equation now write the augmented matrix so here 1 -1 -1 on the right side we have 2 .5 on the second equation we can write 478 17 .8 and on the third equation we can write here 0 minus 2 1 and 0 .3 now we want to make 0 at this element so here first row is as it is here 4 minus 4 is 0 right sorry we have forgot the operation that is r2 minus 4 r1 right this is our operation now here 4 minus 4 is 0 7 minus 4 is 4 that is 3 8 minus 4 is 4 17 .8 minus 10 that is 7 .8 and here third row is as it is now interchange second and third row so here r2 interchange r3 write the third row at second place now write the second row at third place now we want to make zero at here so for this rotation is r3 plus 3 by 2 times r2 right so our new matrix is 111 that is our first row is as it is second row is also as it is here 0 0 5 .5 and on the right side we have 8 .25 now from the third row we can write here 5 .5 z is equal to 8 .25 so here z so here z is equal to 8 .25 by 5 .5 which is equal to 1 .5 from the second row we can write 2y plus z is equal to 0 .3 right so your negative 2y is equal to negative z plus 0 .3 here z is equal to 1 .5 negative 1 .5 plus 0 .3 which is equal to negative 1 .2 so here your y point y is equal to 0 .6...

Question

Please give Ace some feedback