Algebra 2 word problem help ?
The tens digit of a two-digit positive integer is 2 more than three times the ones digit .if the digits are interchanged ,the new number is 13 less than half the given number find the given integer ( hint : let x =tens place digit and y=ones -place digit then 10x + y is the number)
Comments
The first sentence translates almost verbatim to
x = 2+ 3y
If 10x + y is the original number, then 10y + x is the number resulting from interchanging the digits. The second sentence says
10y + x = ½(10x + y) - 13
Multiply both sides of this by 2 to get rid of the fraction:
20y + 2x = 10x + y - 26
Simplify:
19y = 8x - 26
So you have the system
x = 2 + 3y
19y = 8x - 26
Use the first equation to substitute for x in the second equation:
19y = 8(2 + 3y) - 26
19y = 16 + 24y - 26
19y = 24y - 10
10 = 5y
2 = y
x = 2 + 3y = 8
So the original number is 82.