the tens digit of a two digit number is five more than the units digit. the number itself is equal to the sum of the digits multiplied by 8. what is the number?
To find the two-digit number, we can set up equations based on the given information.
Let's assume the tens digit is 'x' and the units digit is 'y'.
According to the first condition, the tens digit is five more than the units digit, so we can write the equation:
x = y + 5
According to the second condition, the number itself is equal to the sum of the digits multiplied by 8, so we can write the equation:
10x + y = 8(x + y)
Now, let's solve these equations simultaneously to find the values of 'x' and 'y'.
Substituting the value of 'x' from the first equation into the second equation:
10(y + 5) + y = 8(y + 5 + y)
10y + 50 + y = 8(2y + 5)
11y + 50 = 16y + 40
11y - 16y = 40 - 50
-5y = -10
y = 2
Now, substituting the value of 'y' back into the first equation to find 'x':
x = y + 5
x = 2 + 5
x = 7
Therefore, the tens digit 'x' is 7 and the units digit 'y' is 2.
Hence, the number is 72.
t = u+5
10t+u = 8(t+u)
Now solve for t and u, the tens and units digits.