 In this video, I wanna do another question involving some simple interest type problems, but this one's a little bit different than the ones we saw before here. So we have an individual who's gonna be investing $10,000 into two separate accounts. The first account has an APR of 5%, and the second account has an APR of 6%. Now tell me where those accounts are, I would love to find that. In 2020, those are amazing interest rates. But anyways, we have these two accounts. Now let's suppose that for whatever reason, our individual cannot invest all 10,000 into the 6%. So some is placed in the 5% account, some is placed in the 6% account. If our person made $560 of interest in that first year, how much money did the individual invest in the two accounts? So notice we actually have like two unknowns in this situation. We have some X value, which we'll say is the number of dollars say in the 5% account. And then we also have another variable Y, which is the number of dollars in the 6% account. We have two unknowns in this situation. This isn't something we've seen a lot in this series already, but we can handle this nonetheless. Cause some things we know are the following. The total amount in the two accounts is $10,000. So we know that X plus Y equals 10,000. More specifically, this tells us that Y equals 10,000 minus X. So we really don't need the variable Y because we know the other number is just gonna be 10,000 minus X. So because of the simple interest formula, we know that interest is equal to principal times rate times time. And so here X is that principle we placed in the 5% account. So we're gonna have 5% times one year times however much we invested, which is X. Then we have the 6% account, which also invested for one year. And we times that by Y, but Y is just 10,000 minus X. And the interest is gonna equal 560. So this equation right here then tells us how much money, well, this gives us an equation of interest. And if we solve for X, which is a linear equation, we can then find out how much was invested in the 5% account. There are some decimals playing around here. So notice that this thing will look like, well, if you don't want decimals, you can always times both sides of the equation by 100. You just have to make sure you do it to both sides, which basically has the effect that you're just gonna move the decimal over by two places. Like so, if you don't want decimals, that's a very nice way to fix this thing up. So we end up with 5X is equal, 5X plus six times 10,000 minus X this is gonna equal 560 and then two more zeros. So 56,000, that's a way of working that way. And so then distribute the six right here, we're gonna end up with 5X plus 60,000 minus 6X is equal to 56,000. So I would combine the X's together. This gives you a negative X plus 60,000 equals 56,000. Subtract 60,000 from both sides, you're gonna get negative X equals negative 4,000 and divide by negative one is the X equals 4,000. This means that our individual invested 4,000 into the 5% account, which means that then they invested $6,000 into the other account. Remember, 10,000 take away 4,000, 6,000. And so we then can conclude here that this person, they invested, this person invested $4,000 at a 5% rate, whoops, apparently it bumped the page down there, at a rate of 5% and invested $6,000 at a rate of 6%. I guess I should say they invested, it already happened, right? So our individual here invested $4,000 at a rate of 5% and $6,000 at a rate of 6%.