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# Age word problem: Ben & William

Sal solves the following age word problem: William is 4 times as old as Ben. 12 years ago, William was 7 times as old as Ben. How old is Ben now? Created by Sal Khan.

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• i don't understand age word problems please if you have any advice ,recommendations answer this question because I've tried many different websites but i don't seem to get how to solve age word problems . • I feel the crux to understanding Sal in this is that 4b-12 is already 7 times as old as Ben's b-12.

That is why he multiplied Ben's (b-12) by 7, so it can equal to William.

I guess I'm sorta saying the 7 times is already applied to the equation right from the beginning. So you have to compensate by multiplying Ben's past age by 7 to equal William's.

Therefore 7*(b-12) = 4b-12 • Can someone help explain this to me? I need help with these kinds of things. • Does anyone have a quick way to calculate division with big numbers like 256/4? (I know its 64 so don't JUST give me the answer) I could do the 72/3 in my head but if there is a good way to do those types of division mentally I'd be glad to hear it. • There are many tips and tricks to dividing numbers in your head.
In your example, 256/4 is the same as 256/2/2 (you can plug this into your calculator to check). So, in reality all you have to do is halve the number twice. Ex: 256->128->64, which is easier to do in your head than doing brute force dividing. There is no quick way to divide by 3 other than just doing it the long way in your head, but there is a divisibility rule (a rule that tells you if 3 can evenly go into a number) for it. If you add up the digits of the number you are trying to divide by 3, and the sum of the digits is divisible by 3, the entire number is divisible by 3. With your number, 72 you can add the digits. 7+2=9. 9, we know, is divisible by 3, so 72 is divisible by 3. This divisibility rule works for all numbers.
• Couldn't you make an equation differently and end up with the same answer? Like I got the equations w=4b and w-12=7b and solved using substitution but didn't get the correct answer? Why? • You have a mistake in your 2nd equation.
"b" represents Ben's current age. When you create the 2nd equation, both Williams and Ben's ages need to be 12 years younger. So, your 2nd equation need to be: `w-12 = 7(b-12)`
Hope this helps.
• At ; I don't understand why for William (12 years ago column) it's 4b-12 and not just 7b? • Think of it this way: Pretend William is 6 years old and Ben is 2, so Will is 3 times the age as Ben, so the equation is (3)2=6, the 2 is Ben's age, the 3 is how many times Ben's age goes into Wills, and the 6 is Will's age. Now, since the real question says that William is 7 times as old as ben, we can set up the equation as this: 7(b-12) = 4b-12. B-12 is Ben's age 12 years ago and 4b-12 is Will's age 4 years ago.
• Wait a sec...if 12 yrs ago, William was 7x as old as Ben, and they both have a birthday every year, shouldn't he stay 7 times older? And, i would understand if the 7 was instead an even number. But 7? I don't really get that.
(1 vote) • If I am 12 now, and my younger brother is 4 years old, then next year, I will be 13 (at the end of the year), and my brother will be 5. Before, I was 3 times as old as my brother, now, I am only 2.6 times as old as him. So the ratio of the ages will change over time; however, the difference between 2 peoples ages will stay the same.
• I still have ZERO idea on how to do this. Can u suggest other videos that might help and include the link? • I've been trying to figure this out for the past couple of months and I'm nowhere near to understanding what variables to plug in. I've been trying to figure this particular problem out with no success:

John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three times as old as Alice. How old is Peter now?

Any thoughts?  