Its kinda hard
asked May 23 in Word Problem Answers by Amelia Yvette (120 points)

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1 Answer

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

‚ÄčAns: number is n = 45

answered May 23 by Fermat Level 11 User (76,040 points)
Thanx
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