*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**

Thanx

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