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Mathematics 20 Online
OpenStudy (anonymous):

The difference between the digits in a two-digit numeral is 3. The units' digit is twice the tens' digit. Find the numeral

OpenStudy (freckles):

do you know what difference between m and n means?

OpenStudy (anonymous):

What

OpenStudy (freckles):

So you never heard of the word difference, right?

OpenStudy (freckles):

the difference between m and n means m-n

OpenStudy (anonymous):

I have...but in this case I'm going to use 2*t (units digit) -t(tens digit)

OpenStudy (freckles):

pretend mn is a two-digit number where m is the ten's digit and n is the one's digit therefore mn can be written as 10m+n anyways... you are given the difference of m and n to be 3 so you have m-n=3 from the first sentence

OpenStudy (freckles):

The units' digit is twice the tens' digit. do you know how to setup this equation style?

OpenStudy (freckles):

remember we let n be the units digit and we let m be the ten's digit so this is really saying n is twice m

OpenStudy (freckles):

can you show me what that looks like as an equation

OpenStudy (anonymous):

10m-2*10m

OpenStudy (anonymous):

=3

OpenStudy (freckles):

? I'm just asking you to write n is twice m as an equation

OpenStudy (anonymous):

n=2m

OpenStudy (freckles):

perfect!

OpenStudy (freckles):

so we have the following two equations: m-n=3 and n=2m

OpenStudy (freckles):

and actually to avoid a negative tens digit cause it sorta doesn't make sense to me here I'm going to say this instead you know since n is larger than m n-m=3 n=2m anyways we can plug the second equation into the first equation giving us 2m-m=3 can you solve for m?

OpenStudy (freckles):

2-1=1 so 2m-m=?

OpenStudy (anonymous):

I know lol...but does that mean that you don't have to worry about multiplying the tens times ten

OpenStudy (freckles):

why are you doing that?

OpenStudy (anonymous):

Because in the previous questions I was given here like 10m + n is the original. They are saying that 10*m is value of the tens digit

OpenStudy (freckles):

we are given the difference of the digits is 3 and that one digit is twice another digits can only be 0,1,2,3,4,5,6,7,8,9 not more or less

OpenStudy (freckles):

m is the value of the 10 ten's digit n is the value of the 1's digit the value of the number is 10m+n

OpenStudy (freckles):

we haven't been giving the value of the number

OpenStudy (freckles):

we are only talking about the digits right now to find the number

OpenStudy (freckles):

example: what can I say about the digits in 41 well I can say the ten's digit minus the one's digit is 3 and that the ten's digit is 4 times the one's digit

OpenStudy (freckles):

So if I wanted to make up a problem and get 41 as an answer: It would go like this: The difference between the digits in a two-digit number is 3. The ten's digit is four times the one's digit. So the equations would look like this: Let mn be the number representation of what we are looking for where m is the ten's digit and n is the one's digit. We are given m-n=3 and that m=4n Pluggin the second equation into the first gives 4n-n=3 3n=3 so n=1 now since m=4n then m=4(1)=4 so mn=41

OpenStudy (anonymous):

Ohhhhhhh

OpenStudy (anonymous):

I see now

OpenStudy (freckles):

yea they are not talking about what value the digit holds they are just talking about the digit

OpenStudy (anonymous):

Yeah

OpenStudy (freckles):

like yes in mn the m value is 10m but they are just about m when they say ten's digit

OpenStudy (freckles):

n-m=3 n=2m So you understand our equations look like this?

OpenStudy (freckles):

for our problem

OpenStudy (freckles):

lol this is probably dumb to point out but when I write mn above I hope you know I don't mean the product of m and n like mn is suppose to represent a number where m is 10's digit and n is 1's digit but I already said this but just in case it got lost up there I wanted to say it again

OpenStudy (anonymous):

Cause in the end it will be 41...I see okay 4*10 and 1*1 Yes I do understand those equations

OpenStudy (freckles):

cool stuff

OpenStudy (anonymous):

Thanks man

OpenStudy (freckles):

np

OpenStudy (freckles):

if you want to do your problem and I check your values for m and n I can

OpenStudy (anonymous):

M is 1 N is 2

OpenStudy (anonymous):

21 is the numeral

OpenStudy (freckles):

let's see I think something happened because the difference there isn't 3

OpenStudy (anonymous):

Ahh

OpenStudy (freckles):

n-m=3 n=2m so you plugged second equation into first equation giving you 2m-m=3

OpenStudy (freckles):

so m=?

OpenStudy (anonymous):

😂 sorry I'm being slow M is 1

OpenStudy (anonymous):

Isn't it

OpenStudy (freckles):

n-m=3 since n=2m we can write this as 2m-m=3 but we know 2m-m=m so we have m=3 since 2m-m=3

OpenStudy (freckles):

and then since you know n=2m then you can replace m with 3 and find n

OpenStudy (freckles):

m=3 n=2m=2(3)=?

OpenStudy (anonymous):

M is 3

OpenStudy (freckles):

right and n=?

OpenStudy (anonymous):

6

OpenStudy (freckles):

mn=36 notice the difference of 6 and 3 is 3 and that 6 is twice the number 3 is we did it

OpenStudy (anonymous):

So meaning the numeral is 36

OpenStudy (freckles):

yep

OpenStudy (anonymous):

Okay noooow I think I got it

OpenStudy (freckles):

Do you want to try solving another one similar to it? I can make one up.

OpenStudy (freckles):

If you want to here is another: The difference between the digits of a 2-digit numeral is 6. The one's digit is three times the ten's digit. What is the numeral?

OpenStudy (anonymous):

39 is the numeral

OpenStudy (freckles):

omg omg you did it

OpenStudy (freckles):

good job you

OpenStudy (anonymous):

😂😂😂 Loool Thanks though

OpenStudy (freckles):

np

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