SOLUTION: A three digit number divisible by ten has a hundreds digit that is one less than its tens digit. The number is 52 times the sum of its digits. Find the number.
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Question 393090: A three digit number divisible by ten has a hundreds digit that is one less than its tens digit. The number is 52 times the sum of its digits. Find the number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A three digit number divisible by ten has a hundreds digit that is one less than its tens digit. The number is 52 times the sum of its digits. Find the number.
:
We know the last digit = 0
:
Let the number = 100x + 10y + 0
:
" a hundreds digit that is one less than its tens digit."
x = y - 1
:
The number is 52 times the sum of its digits.
100x + 10y = 52(x+y)
100x + 10y = 52x + 5y
100x - 52x = 52y - 10y
48x = 42y
Replace x with (y-1)
48(y-1) = 42y
48y - 48 = 42y
48y - 42y = 48
6y = 48
y =
y = 8
then
x = 7
:
780 is the number
:
:
confirm this in the statement:
"The number is 52 times the sum of its digits."
780 = 52(7+8)
780 = 52(15)
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