The units’ digit of a two-digit number is 7 more than the tens’ digit. If 26 is added to the number, the result obtained is five times the sum of the digits. Find the number.
substitute t+7 for u and you get
10t + t+7 + 26 = 5(t + t+7)
11t + 33 = 10t + 35
t = 2
so, u=9
and the number is 29
check: 29+26 = 55 = 5(2+9)
how to crank it out
To find the two-digit number, let's assign variables to the tens' digit and the units' digit.
Let the tens' digit be "x", and the units' digit be "y".
From the given information, we can form two equations:
1) "The units' digit of a two-digit number is 7 more than the tens' digit":
y = x + 7
2) "If 26 is added to the number, the result obtained is five times the sum of the digits":
10x + y + 26 = 5(x + y)
Now we have a system of two equations.
To solve this system, we can substitute the value of y from the first equation into the second equation:
10x + (x + 7) + 26 = 5(x + (x + 7))
Simplify the equation:
10x + x + 7 + 26 = 5(2x + 7)
11x + 33 = 10x + 35
11x - 10x = 35 - 33
x = 2
Now substitute the value of x back into the first equation to find y:
y = x + 7
y = 2 + 7
y = 9
Therefore, the tens' digit is 2, and the units' digit is 9. The two-digit number is 29.
u = t+7
10t+u + 26 = 5(t+u)
now just crank it out.