SOLUTION: the ratio of the tens digit to the units digit of a two-digit number is 1 to 4. the number formed by reversing the digits is 2 less than 3 times the original number. find the orig

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Question 203394: the ratio of the tens digit to the units digit of a two-digit number is 1 to 4. the number formed by reversing the digits is 2 less than 3 times the original number. find the original number.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the ratio of the tens digit to the units digit of a two-digit number is 1 to 4.
the number formed by reversing the digits is 2 less than 3 times the original number.
find the original number.
:
Let x = the tens digit
Let y = units
then
10x + y = the original number
:
"the ratio of the tens digit to the units digit of a two-digit number is 1 to 4."
x%2Fy = 1%2F4
cross multiply
4x = 1y
:
"the number formed by reversing the digits is 2 less than 3 times the original number."
10y + x = 3(10x+y) - 2
:
10y + x = 30x + 3y - 2
:
10y - 3y = 30x - x - 2
:
7y = 29x - 2
Substitute 4x for y:
7(4x) = 29x - 2
28x = 29x - 2
+2 = 29x - 28x
x = 2
then
y = 4(2)
y = 8
:
28 = the original number.
;
:
Check solution in the statement:
"number formed by reversing the digits is 2 less than 3 times the original number."
82 = 3(28) - 2
82 = 84 - 2