A two digit number is formed by either substracting 17 from nine times the sum of the digits or by adding 21 to 13 times the difference of the digits .find the number
If the digits are a and b, then
10a+b = 9(a+b)-17 = 13(a-b)+21
a-8b = -17
-3a+14b = 21
(a,b) = (7,3)
The number is 73
Five times the sum of a number and 17 is at most 28 .
i've been searching for the same question, with little to no luck. one website says it's 83, over here someone says it's 73.
To find the two-digit number, we need to set up and solve an equation based on the given information.
Let's assume the tens digit of the number is represented by 'x' and the units digit is represented by 'y.'
According to the given information:
1) "A two-digit number is formed by subtracting 17 from nine times the sum of the digits":
This can be expressed as 10x + y = 9(x + y) - 17.
Expanding this equation, we get: 10x + y = 9x + 9y - 17.
2) "A two-digit number is formed by adding 21 to 13 times the difference of the digits":
This can be written as 10x + y = 13(x - y) + 21.
Expanding this equation, we get: 10x + y = 13x - 13y + 21.
Now we have a system of two equations:
1) 10x + y = 9x + 9y - 17
2) 10x + y = 13x - 13y + 21
To solve this system, we can subtract equation 1 from equation 2:
(10x + y) - (10x + y) = (13x - 13y + 21) - (9x + 9y - 17)
This simplifies to:
0 = 4x - 4y + 38
Next, we rearrange the terms:
4x - 4y = -38
Now we can divide the entire equation by 4 to simplify further:
x - y = -9.5
Since we are dealing with a two-digit number, the tens digit cannot be negative or fractional. Therefore, we know that x must be greater than y.
To find the integer values of x and y, we will try different combinations that satisfy the equation x - y = -9.5.
If we let x = 0 and y = 9, the equation becomes 0 - 9 = -9, which is not equal to -9.5.
If we let x = 1 and y = 0, the equation becomes 1 - 0 = 1, which is not equal to -9.5.
If we let x = 2 and y = 1, the equation becomes 2 - 1 = 1, which is valid.
Therefore, the two-digit number can be found by combining the values of x and y: 21.
Hence, the two-digit number is 21.