SOLUTION: a two digit number has a value two more than six times the sum of its digits. the tens digit is one more than the units digit. find the number
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Question 618287: a two digit number has a value two more than six times the sum of its digits. the tens digit is one more than the units digit. find the number
Answer by dragonwalker(73) (Show Source): You can put this solution on YOUR website!
Let us say that the unit digit is 'u' and the tens digit is 't'
The number can then be written as 10t + u
We know that 10t + u - 2 = 6t + 6u
also:
t = u + 1
substitute t from second equation into the first full equation:
10(u+1) + u - 2 = 6(u+1) + 6u
10u + 10 + u - 2 = 6u + 6 + 6u
rearrange so all 'u's on left and numbers on right. Remember to change the sign if you change the side that a value is on:
10u + u - 6u - 6u = 6 + 2 - 10
-u = -2
so:
u = 2
so if u=2 then t must be equal to 3 (u+1=t)
the number is 32
to check:
Sum of its digits times six is: 2+3 = 5 times by 6 = 30.
the number is 32 which is indeed two more than 30
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