SOLUTION: A three-digit number divisible by 5 has a hundreds digit that is 2 more than the tens digit. If the number is 43 times the sum of the digit, what is the number?
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Question 179134: A three-digit number divisible by 5 has a hundreds digit that is 2 more than the tens digit. If the number is 43 times the sum of the digit, what is 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 5 has a hundreds digit that is 2 more than the tens digit. If the number is 43 times the sum of the digit, what is the number?
:
Let x = 100's digit
Let y = 10's digit
units digit = 0 or 5
:
" hundreds digit that is 2 more than the tens digit."
x = y + 2
:
Units = 5:
"the number is 43 times the sum of the digit,"
100x + 10y + 5 = 43(x + y + 5)
100x + 10y + 5 = 43x + 43y + 215
100x - 43x + 10y - 43y = 215 - 5
57x - 33y = 210
:
Substitute (y+2) for x
57(y+2) - 33y = 210
57y + 114 - 33y = 210
57y - 33y = 210 - 114
24y = 96
y =
y = 4
then
x = 6
:
the number: 645
:
check 43(6+4+5) = 645
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