Number problem!

[ForkingBullshirt]

Hi!
Ds has come across this problem online and has asked me to explain how to work it out...I'm stumped!

*The difference between two numbers is 20. The result of dividing the larger number by the smaller number is 9. What are the numbers?

Anyone smarter than me about?? ds is now amusing himself elsewhere but this is really bugging me!

I had to ask DH and he thinks the numbers are 22.5 and 2.5
Do they have to be whole numbers?

2.5 and 22.5

Thanks!
It doesn't say if the numbers have to be whole.

Can I ask how it was worked out? I'd like to show ds this so he can learn to do it himself (because I'm clearly no help!)

Say the numbers are b and s

b -s = 20

b/s = 9 => b=9s

substituting into the first equation 9s-s=20 => 8s=20 s= 2.5
substituting back to the first equation b-2.5 = 20 => b=22.5

So big number is 22.5 and small is 2.5

x + 20/x =9

x + 20=9x

8x=20

x = 20/8

x = 2.5

Therefore larger no. = 2.5+20

Thank you!

The numbers are x and y
x + 20 = y
9x = y
x + 20 = 9x
20 = 8x
x = 20 / 8
x = 2.5
y = 22.5

Cross post

I'm curious - Is elementary algebra not taught in UK schools?

Cote Of course it is taught, as is shown by the posters who can solve the problem.

But some people haven't used it for years or didn't really understand it well the first time, so it is hardly surprising that some people won't know the way to solve this problem.

And as to whether or not the DS should know how to solve the problem, it rather depends on the age & ability.

Hi!

Ds is 7. He's 'ahead' in maths and is always pushing himself, hence looking at problems online.

As for me...I'm just not very good at it . Actually that's not completely true. Its just been a while...

Thanks again! Ds has been in his element today and has started reading up on the basics of algebra.

He could also solve this by trial and error.

10 & 20 => when divide leads to 3
20 & 40 => 2. Going in the wrong direction
5 & 25 => 5 getting there
1 & 21 => 21 too far
2 & 22 => 11 nearly right
3 & 23 => 7.666 on the other side again
2.5 & 22.5 => 9 DONE.

Playing around like that will give him a 'feel' for numbers, which is helpful. It will help him have a feel as to whether an answer 'sounds right' or whether he needs to look again to see if there is a mistake.

Thanks so much Teen.

He really is quite able in mathematics (from what I can tell...)
I'll show him this tomorrow and I'm certain he'll be online again looking up more stuff to practice.

If he has a calculator (or can do division well), get him to see what 1/7, 2/7, 3/7,...6/7 look like when they are decimals.

Also if he doesn't know already:

Test for divisibility by 9 : Add up the digits and if total is divisible by 9 then the number is.
1034676 >1+0+3+4+6+7+6=27=>2+7=9

test for divisibility by 11: Add and subtract alternate digits, if total is zero or divisible by 11 then the number is
8745 -> 8-7+4-5=0

These have always pleased me greatly. (& I had to prove the divisibility tests in my university interview).

Start saving for uni now. Friends dc was the same at maths, did it for ‘fun’ she’s now at Cambridge.