a number consist of two digits of which tens digit exceeds the unis digit by 7 the number itself is equal to 10 times the sum of its digit find the number
unit digit --- x
tens digit --- x+7
10(x+7) + x = 10(x + x+7)
10x + 70 = 20x + 70
10x = 0
x = 0
so the number is 70
a number consists two digit number of which tens digit exceeds the unit digit 7. the number itself is equal of 10 times the sum of its digits find the number
Let's solve this step-by-step.
Let's assume that the tens digit is represented by 'x' and the units digit is represented by 'y'.
According to the given information, the tens digit exceeds the units digit by 7, so we can write the equation: x = y + 7.
The number itself is equal to 10 times the sum of its digits, so we can write the equation: 10x + y = 10(x + y).
Substituting the value of x from the first equation into the second equation, we get: 10(y + 7) + y = 10(y + (y + 7)).
Simplifying this equation, we can solve for y: 10y + 70 + y = 10(2y + 7).
Simplifying further, we have: 11y + 70 = 20y + 70.
Subtracting 11y from both sides, we get: 9y = 0.
Dividing both sides by 9, we get: y = 0.
Substituting the value of y back into the first equation, we get: x = 0 + 7.
Therefore, the number is 07.
To solve this problem, let's assign variables to the unknowns:
Let's represent the tens digit with the variable x, and the units digit with the variable y.
According to the information given in the question, we know that:
"The tens digit exceeds the units digit by 7", which can be written as:
x = y + 7
"The number itself is equal to 10 times the sum of its digits", which can be written as:
10x + y = 10(x + y)
Now, we can solve the system of equations to find the values of x and y.
Substituting the value of x from the first equation into the second equation, we have:
10(y + 7) + y = 10(y + 7 + y)
Expanding the equation:
10y + 70 + y = 10y + 14y + 70
Combining like terms:
11y + 70 = 24y + 70
Subtracting 11y and 70 from both sides:
0 = 13y
Dividing both sides by 13:
y = 0
Now, substitute the value of y back into the first equation to solve for x:
x = y + 7
x = 0 + 7
x = 7
Therefore, the number consists of the digit 7 in the tens place and 0 in the units place, making the number 70.