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### Course: 8th grade (Illustrative Mathematics)>Unit 4

Lesson 8: Lesson 9: When are they the same?

# Age word problem: Arman & Diya

Sal solves the following age word problem: Arman is 18. Diya is 2. How many years will it take for Arman to be 3 times as old as Diya? Created by Sal Khan.

## Want to join the conversation?

• I understand the video, but I have trouble answering the problems on my own. I don't understand which one you are supposed to times and how you are supposed to tell. For example: Daniel is 40 years older than Vanessa. 12 years ago, Daniel was 3 times older than Vanessa.
Which part of the equation do you times? I thought it was Vanessa's part (the smaller one) to make it the same amount as Daniel's but I keep making errors and am not getting anywhere.
I know the example I have made does not make any sense, but if you could just show the process and how to put each part into the equation, I'd be grateful as I'm getting very frustrated!
• Don't worry! There's always something you don't know!
It takes patience and courage! One day you will master it!

@Lizzie Whittington, I can't answer your question because there is no question. But I can tell you something. Sometimes you have to think out of the box and answer the question, sometimes you don't fully understand the question, then you read the question again, again and again until you understand it. Which part of the equation do you times? Well sometimes it involves you reading in on perspective or another. Once you fully understand it, you can translate it into algebraic language.

You just need to understand what the question is saying
• I know how to do the math really well, but when it comes to word problems I get stuck and don't know what to do. Is there a specific method or any techniques I can do to set an equation or a word problem up?
• The trick with word problems is thinking, 'what is the question asking me?' 'What information do I have?' 'What information is relevant?' Look for key words which could relate to operations, I.e if the question asks about difference you'll probably need to subtract, etc. this is the basic premise I use to teach word problems. Look up Newman's Prompts. It's a series of questions to ask yourself to breakdown word problems.
• I cannot understand one of the practice questions:
"Micheal is 12 years older than Brandon. Seventeen years ago, he was 4 times as old as Brandon."

So I first did m=b+12, representing Micheal's Age. Then I wrote the equation m-17=4b, representing how 4 times Brandon's age was equal to Micheal's age 17 years ago. So, I plugged my m into the 2nd equation, and got this:

b+12-17=4b
-5=3b
b=-5/3

Obviously that's wrong, but I don't understand how I could have constructed the equation incorrectly.
• The mistake is in your 2nd equation. Both people are 17 years younger. You only have Mike as 17 years younger.
Correct 2nd equation: m-17 = 4(b-17)
Hope this helps.
• I literally am so confused. I have no idea how to do this and I don't even know what I don't know. Help please!
• You just need to assume the unknown as x. Then, try to build a linear equation. Try to solve that equation.
• Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I will be three times as old as you will be". Solve it algebraically...
• If A is Aftab and D is daughter, then A -7 = 7(D-7) and A+3 = 3(D + 3). Try to solve this system of equations. I assume the question is what are their ages now.
• I dont understand when sal says: We wanna solve for y, such that 18 plus y is going to be equal to 3 times, 2 plus y. Can someone explain and help me with this please {:(
• 18 + y = 3 ( 2 + y ) : step 0, write out the equality
18 + y = 6 + 3y : step 1, apply the distributive property of multiplication
18 + y - y = 6 + 3y - y : step 2, subtract y from each side of the equation
18 = 6 + 2y. : step 2.5, the result of step 2
18 - 6 = 6 + 2y - 6 : step 3, subtract 6 from each side
12 = 2y : step 3.5, the result of step 3
Now, what' s the answer? I'm tired of typing!
• how is this possibke
• I did it a different way:

3(x+2) - 18 = x

3(x+2) is arman's age 'then'.

Diya is 2 now, so add some year 'x' and multiply by 3 will give armans age at the time. (I could write 2+x but it was just easier to write it as I did for me personally as I thought changing addition order will not change the sum)

I know Arman is 18 and therefore, the difference between his age then vs his age now will give the years between them i.e. the years it took.

But for some of the equation, I ended up with minuses so I wonder if my equation is still correct in terms of what I was trying to show?

3(x+2) - 18 = x
[multiply out the brackets]
3x + 6 - 18 = x
[Brackets multiplied]
+ 6 - 18 = - 2x
[minus 3x from both sides]
- 12 = - 2x
[divide by -2 from both sides]
6 = x