You inherit one million dollars you invest it all in three...

You inherit one million dollars. You invest it all in three accounts for one year. The first account pays 5% compounded annually, the second account pays 6% compounded annually, and the third account pays 4% compounded annually. After one year, you earn $52,500 in interest. If you invest 3 times the money into the account that pays 5% compared to 4%, how much did you invest in each account? Investment in 4% account: Investment in 5% account: Investment in 6% account:

Transcript

00:01 If you inherit a million dollars and you invested in three accounts for a year, we're going to figure out how much was invested in the account at 4%, how much in the account at 5 % and how much in the 6 % account.

00:14 We're going to write our systems of linear equations as we go.

00:19 And so we know it's a million dollars and there's three accounts.

00:23 So we're going to call those accounts x, y, and z.

00:25 So x plus y plus z has to equal that $1 million, that total amount we're investing.

00:30 So that's our first equation.

00:34 The first account pays 5 % compounded annually.

00:37 Okay, so 0 .05.

00:39 We're writing our percentages as a decimal x plus the second account pays 6 % compounded annually, 0 .06y, plus, and the third account pays 4 % compounded annually, 0 .04z.

00:58 After one year you earn 52 ,500 in interest.

01:03 So it's going to equal that 52 ,500.

01:07 So we have our second equation.

01:10 If you invest three times the money into the account that pays 5 % compared to 4%.

01:15 So we're going to get 3z, three times that 4 % account equals our 5 % account x.

01:23 How much money? how much did you invest in each account? so now i have three unknowns and three equations.

01:28 I'm going to start by substituting in the 3z for x.

01:34 So we get 3z plus y plus z equals 1 million.

01:45 I'm going to combine like terms.

01:47 We get 4z plus y equals 1 million...