This is just confusing...?

Question

so i helped my brother with the rest of the "distance=rate*time"
but this is weird...

The units digit of a two digit number is twice the tens digit. if the digits are reversed, the new number is nine less than twice the original number. what is the original two-digit number?

does it have some thing to do with 2x-9???

Answer 1

Don't listen to those who tell you to just guess and check.

This is a system problem meaning that you will multiple equations with multiple variables in them.

Let a be my original two digit number. Let x be the units digit in a and let y be the tens digit in a.

So a looks like yx meaning that yx are NOT being multiplied. I am just writing them next to each other. For example, if a was 56, then y would be 5 and x would be 6.

So a=yx=10y+x

Here are the equations that are derived from the given problem

x=2y
10x+y=2(10y+x)-9

The best way to solve this would be to substitute and we get
10(2y)+y=2(10y+2y)-9 which gives us 21y=24y-9 which then gives us that 3y=9 so y=3. Since x=2y, x=6, so the original number was 36. And you can check it that if I reverse the digit, the number becomes 63 which is precisely 2(36)-9.

Done

Answer 2

Let the tens digit of the number be a and the units digit be b. Then the number itself will be 10a + b. Now, we know the units digit is twice the tens digit, so b=2a. We also know that the number you get when you reverse the digits (which is 10b + a) is 9 less than twice the original number, so 10b+a = 2(10a+b) - 9. This gives you the following system of equations in two variables:

b=2a
10b+a = 2(10a+b) - 9

Solving by substitution:

10(2a)+a = 2(10a+(2a)) - 9
20a + a = 20a + 4a - 9
-3a = -9
a=3

So b=2*3 = 6, and the number in question is 36.

Answer 3

Well i'd solve it this way, you must find a two digit numbers xy and you know:

1. The units digit (y) is tow times de tens digit (x)
y=2x
2. I will call the number xy a constant C

10*x +y = c

3. When the digits are reversed, the new number is nine less than 2times xy (c)

10*y + x= 2*c - 9

Solving this system, you get that the number is 36.

Answer 4

Let 10t + u be a 2 digit number. We know that

2u = t

Now reverse the digits in the number, we have 10u + t, and we know that

10u + t + 9 = 10t + u (the new number is nine less than twice the original number)

So, substitute 2u for t and we have

10u + 2u + 9 = 10(2u) + u
12u + 9 = 20u + u
9 = 21 u - 12u
9 = 9u
u = 1
Since 2u = t, we have t = 2

10t + u = 10(2) + 1 = 21

HTH

Charles

Answer 5

10(x) + (2x) would be the first number.
10(2x) + (x) = 2(10(x) + (2x)) - 9
21x = 24x - 9
x = 3

So, the ten's digit of the original number is '3' and since the one's digit is twice the ten's, the one's digit would be '6'.
Check: 36 reversed is 63, 36 doubled is 72 and minus 9 is 63

Answer 6

the answer i got was 36
i just used guessed and check.
i started with 24 and it was wrong so i chose 36.
yes it does use 2x-9 because you substitue the original number as x.

2(36)-9=72-9=63 which is the reverse of 36 :)

Answer 7

2 x -9 = -18

Answer 8

No you have to use common sense. The answer if 36.
A possible way to do it are going through all combinations. (There are only 4!)