Question 241901
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 = {{{5/2.5}}}
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