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Mike is 5 years older then Joan. In ten years, the sum of their ages will be 57 . What are their present ages?

$$J=16, M=21$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

03:06

Gary is 5 years older than…

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02:25

Pat is 20 years older than…

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.

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