CLLCLLPICOC1L do-o.Laura is 25 years older than Larry In 1O years from now; Laura will be twice as old as Larry will be. Find their present ages. be 81. What...

Pat is 20 years older than his son Patrick. In 2 years, the sum of their ages will be $90 .$ How old are they now?
$$\begin{array}{|l|l|} \hline \text {
} & \hline \text { Now } & \text { In 2 Years } \\ \hline \text { Patrick } & x & \\ \hline \text { Pat } & & \\ \hline \end{array}$$

Here we are. Given that Gary is five years older than Harry on 29 years ago, Gary was twice the or less Harry. So we have to find the age of Gary and Harry. So let us assume that the current age off Gary is equal to X Onda. The age off Harry is acquitted away. No, it is you and that Gerry's five years older than Harry. That means X is equal to y. Plus, Fife, begin to rewrite this equation X Rewrite this equation as X minus Y is equal to five on the second sentiment is given a 29 years ago. Get it was twice the or less hurry. That means 29 years ago means X minus 29 is twice This is the age off Getty his twice the age off. Harry, that means two times off of I minus 29. So from here we get X minus 29 physicals toe. So I, minus 58 Oregon, right. This equation as X minus two way is equal to negative 29. So we have opened to equation. This is the first equation on. This is the second English in. Now we're going to solve these two equation by using the Kraemer school, and we know that the value of X is equal to the expertise. By using the Cameroon on Why is recalled stood divi Obaidi. So first of all vehicles led the value off the so D is it will do the derailment value off 11 minus one minus two average in the coefficient of X In the first column coefficient of find the second column so we'll get the video for DS. Negative one now will calculate the value off DX. It is equipped to five minus 29 negative one negative, too average in the averages value in the first column on the coefficient of y and the second Ghanam. So we'll get the value off D X as negative 39 on finding local cleared the value of Dubai. It will be equals to the regimental really offer 11 five negative 20 name average in the coefficient of X in the first column on average is will you in the second column, so we'll get the value of a D Liars and negative 34. So finally begin right now X records to be exploited to the exodus minus 39 development minus one, which is 39. And why is equal shooter before? So finally, we can conclude there. The age off Gary is 39 years on a day off. Harry is 30 40 years.

Here. In this problem, we have to find the current age off Gary and Harry, so letters Unit X denotes the current age off Gary on writing notes. The current age off Harry No, The first statement given is that Gerry's five year older than Harry Gary Means X is five years older than Harry means y plus faith. So there's the first equation that were opened next there, saying that 29 years ago, Gary was twice as old as Harry. That means 29 years ago means X minus 29 and this age off Getty. It is a place the age off Harry and means of I minus two in the lane. So you want to simplify this equation? On we get X minus 29 is equals to two way minus 58. All weaken right X minus two way is equals to negative, truly name civic and great decision equation here, X minus two way is equal to negative toe and remained on. We can read this first equation as X minus Y is equal to five. So this was the first on this one. A second equation. Let this be his first, and this Bs Second equation. Now we have to solve these two equation by using the Kraemer zul. We know that by using Cramer's Rule X is equals to be expert D. And why physicals to do everybody? So, first of all, we're going to calculate the value off be so the is equals to the betterment really off one negative one one negative, too. I really like a vision of picks in the first column on coefficient of y in the second column, so you get the value of Diaz negative one. Next look going to calculate the value off the X that will be called Stuart Government. Really off Fife Negative 29 Negative one negative to average in the average is really in the first column on the coefficient of Y in the second column. So look at the value of DX, as in negative 39 I will calculate the value off de vie that will be equals to the detriment value off one one Fife Negative 20 Name I've read in the coefficient off X in the first column on the average Israeli in the second column, so get there early off, devious in negative 34. So X will be equals to the expert E negativity 95 when everyone is 39. Similarly, revival big worlds to 34. So finally we can conclude that age off Getty. Is that your domain? Onda? Age off Harry is turkey ful. So this is the final answer.

All right, So for this question, we have the following information between Mike and Join. We know that Mike is five years older than join, and that in 10 years does some of their ages is going to be 57 on. We're trying to solve their current age. So this is we're gonna used the same principles that we used before where we're going to try to be selling for to unknown variables and these they're gonna be in your equations. And there is to the power of one. We're gonna use the fact that addition and subtraction will under each other, and multiplication and division will under each other too. So we have Mike and join. Mike is five years older than join. So you know that makes current age and just write it down Nights Current age is equal to Joan's plus five because he's five years older than Joanne. And we know that in 10 years, the some off with their agents is gonna be 57. So we have Mike. Plus, Joanne is equal to 57. But it's important to note that this is in 10 years time, so they're both going to be and years old, you're gonna have time to each of them and now and simply substitute. So we have two equations basically, Um, but we're just going to substitute this, Um, because J plus five value here into this m they're going to replace them with J Plus five because we know that em is equal to this. So we're gonna have J plus five so again, which is replaced. Simplified. Um, okay. Plus 10 again is equal to 37. And now we can solve this with our regular rules, simplify, rearrange and then isolate J. So we want we want to get J by itself at the end. So we're gonna have J plus J is just too. Jay. Yeah, those five plus 10 plus 10. So that's 25. We have 25 quick to 57 and we want to get TJ by itself. So we're gonna attract both sides of the equation by 25 five kill. So now we have okay on, then 25 minutes. 25. It's just your old And then we have 57 minus 25 which is just 32. If no, we can simplify this even further we're gonna isolate J, letting both sides of the equation by two. So we're gonna have to get a better way to. We have that k by itself because two divided by two is just one. J J is equal to 32 divided by two. That's simply 16. So we know that case age is 16. We're gonna plug in this value into the original equation to find mix age. So now we have Mike is able to J, which is 16 type. Come with eight is equal to 21. I don't think the ones age 16 mixed age is 21.

So right now we're given that Patricia is 12 years old and her sister is only two. So if we represent Patricia's age is a variable X. We're sorry. Let's represent Bernays. Age is the variable X. So Renee is X years old. Then Patricia is always going to be X plus 10 years old. She's always going to be 10 years older in 12. Minus two. Gives us that 10. So we want to find out when X Plus 10 is going to be equal to two X. So So in order to do that, we can just set up the equation again. X Plus 10 equal 22 acts because we're looking for one. Patricia will be twice Bernays age and X represents Rennais. Age X plus 10 represents Patricia's. So now we're going to solve this equation will subtract X from both sides. I don't leave us with 10 is equal to a single X just to remind you again. X represented rennais age. So Renee will be 10 years old, and Patricia, like we saw before, is 10 years older. So Patricia should again be double her age at this point. But also 10 years older in 10 plus 10 gives us 20. So Patricia will be 20 years