SOLUTION: The tens digit of a given two-digit positive number is two more than three times the units digit. If the digits are reversed, the new number is 13 less than half the given number.

Question 241901: The tens digit of a given two-digit positive number is two more than three times the units digit. If the digits are reversed, the new number is 13 less than half the given number. Find the given integer.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = the tens digit
Let y = the units
then 10x+y = "the number"
:
Write an equation for each statement, just as it says:
:
"The tens digit of a given two-digit positive number is two more than three times the units digit."
x = 3y + 2
:
"If the digits are reversed, the new number is 13 less than half the given number."
10y+x = .5(10x+y) - 13
10y + x = 5x + .5y - 13
10y - .5y = 5x - x - 13
9.5y = 4x - 13
:
Find the given integer.
:
From the 1st statement, replace x with (3y+2) in the above equation:
9.5y = 4(3y+2) - 13
9.5y = 12y + 8 - 13
9.5y = 12y - 5
+5 = 12y - 9.5y
5 = 2.5y
y =
y = 2
then
x = 3(2) + 2
x = 8
:
82 is the number
:
:
Check solution in the statement:
"If the digits are reversed, the new number is 13 less than half the given number."
28 = .5(82) - 13
28 = 41 - 13
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