A number of two digits is such that twice the ten digits is 8 less than seven times the unit digit. When the digits are reversed, the number is decreased by 9. What is the number?

let the tens digit be x, and the unit digit be y

So the number is 10x + y,
the number reversed is 10y + x

10x+y - (10y+x) = 9
9x - 9y = 9
x - y = 1 or x = y+1 **

2x = 7y-8
sub in **
2(y+1) = 7y - 8
2y + 2 = 7y - 8
-5y = -10
y = 2

The number is 32

check:
the number reversed is 23, which is 9 less than 32.
Twice the ten digit is 6
7 times the unit digit = 14, which is 8 less than 6
My answer is correct.

Pls how did you get 32 as the number

Superb

Thanks,but why is it 10x+y and not x+y

To solve this problem, let's assume the ten's digit of the number is represented by "x" and the unit digit is represented by "y".

According to the given information, we can form the equation "2x = 7y - 8", as twice the ten's digit is 8 less than seven times the unit digit.

We can also form another equation based on the second condition, which states that when the digits are reversed, the number is decreased by 9. This can be represented as "10y + x = 10x + y - 9".

Now, let's solve the system of equations:

From the first equation, we can rewrite it as "2x - 7y = -8".

Next, we can rearrange the second equation to simplify it:
10y + x - 10x - y = -9
-9x + 9y = -9

Let's multiply the second equation by 2 to eliminate the "y" terms:
-18x + 18y = -18

Now, we can solve the system of equations using either substitution or elimination.

Substituting the value of "-18x + 18y" from the second equation into the first equation:
2x - 7y = -8
-18y - 18 = -8
-18y = 10
y = -10/18
y = -5/9

Substituting the value of "y" back into the second equation:
-9x + 9(-5/9) = -9
-9x - 5 = -9
-9x = -9 + 5
-9x = -4
x = -4/-9
x = 4/9

Since we are dealing with digits, the values of "x" and "y" cannot be fractions. Therefore, there is no solution to this problem.

In conclusion, there is no number of two digits that satisfies the given conditions.