00:01
If somebody has $500 ,000 to be invested between two funds, fund a, which earns 5 .2 % annually, and fund b, which earns 7 .7 % annually, how should they divide these funds to earn an annual interest income of $34 ,000? so we're going to be using a system of equations here.
00:17
So starting with the first one, we know that whatever funds are put into fund a, plus those funds put into fund b must equal that total $500 ,000 that we're dividing.
00:27
Then we have a second equation which takes into account this annual interest equal to $34 ,000.
00:35
So we have fund a, which we know earns 5 .2 % interest annually, so that's 0 .052 in interest times the funds put into it plus fund b, which earns 7 .7 % interest annually times its funds that are put into it, must equal $34 ,000 annually.
00:58
So now we can start by solving for one of our variables in this yellow equation.
01:02
So let's solve for b real quick.
01:04
So here we see that b is equal to 500 ,000 minus a, and that makes sense.
01:11
Whatever funds we're putting into fund b must be equal to the 500 ,000, that total amount, minus that amount that goes into fund a.
01:19
So we can then plug this into our green equation.
01:21
So we've got 0 .052a plus 0 .077 times b...