SOLUTION: A number consisting of two digits is five times the sum of the digits .If the digits interchange their places ,the new number will be 9 more than the original number .Find the orig

Question 927895: A number consisting of two digits is five times the sum of the digits .If the digits interchange their places ,the new number will be 9 more than the original number .Find the original number
Answer by ptfile(81) (Show Source): You can put this solution on YOUR website!
Let t=tens place
u=units place
10t+u= Original Number
10u+t= New Number
A number consisting of two digits is five times the sum of the digits.
10t+u=5(t+u)
If the digits interchange their places ,the new number will be 9 more than the original number.
10u+t=10t+u+9
9u=9t+9
Divide the whole equation by 9
u=t+1
substitute u with t+1 in the equation 10t+u=5(t+u)
10t+(t+1)=5(t+(t+1))
11t+1=5(2t+1)
11t+1=10t+5
t=4
Solve for u
10(4)+u=5(4+u)
40+u=20+5u
20=4u
u=5
The number is 45.
Check
4+5=9
45/9=5

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