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Age Word Problems - Problem 2

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Zack is 4 years older than Nico. 6 years ago, Zack's age was twice Nico's age. How old are they now?

This is one of those age problems where I need to keep track of their current ages and also their ages in the past because of 6 years ago. So here we go, let's talk about currently.

Currently, Zack is 4 years older than Nico. So you take Nico's age, you add 4 to it and you get Zack's age. I write my z like that a lot of times in Math problems so I can remember that means z, it doesn’t mean 2. It can be really tricky.

Okay, so Nico's age plus 4 is Zack's age. 6 years ago, Zack's age was twice Nico's age, that's tricky. What I'm going to have to do is subtract 6 from each of these guys. Zack's age take away 6 was equals to twice Nico's age take away 6. That was 6 years ago. Once I have it set up like this, I'm ready to do substitution because I have Zack or Z isolated all by itself.

Right here in the second equation instead of z, I'm going to write n plus 4, n plus 4 that was my substitution bit, take away 6 is equal to 2n minus 12, I distributed there. Let's go through and combine like terms n take away 2 equals 2n minus 12, I'm almost done. Subtract n from both sides and add 12 to both sides and I'll be able to see that Nico is 10 now, 10 currently. His current age is 10. That means I can figure out Zack's age also currently. Zack is Nico's age plus 4. So Zack is going to be 10 plus 4 or 14 currently.

Let's just check that out. You can check it in your brain without doing any writing to make sure our answer makes sense. Zack is 4 years older than Nico, okay. 6 years ago well let's think 6 years ago Zack was 8 and Nico was 4. Zack's age was twice Nico's age boom. There is it is how old are they now?

When you're checking your work, you don’t have to write it all out, you can just do it in your head and that helps verify that I did all the problem steps correctly. That's important especially when you're doing lots of substitutions where you might have made a small error along the way.

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