a two digit number in base ten is equal to 5 times the sum of the digits. it is 9 less than the number formed when the digits are interchanged. find the number
Let the two digits be a and b, such that the number n = ab, meaning n = 10a + b, then
n = 5(a + b) (a two digit number in base ten is equal to 5 times the sum of the digits)
n = (10b + a) - 9 (it is 9 less than the number formed when the digits are interchanged.)
Our three equations then are,
n = 10a + b ------------------------ (1)
n = 5a + 5b ------------------------ (2)
n = a + 10b - 9 --------------------- (3)
2*(2) - (1), 5*(3) - (2)
n = 9b
4n = 45b - 45
substituting for n = 9b,
36b = 45b - 45
9b = 45
b = 5, a = 4
Ans: number is n = 45