Answer:
38
Explanation:
Let x = the ones digit, and let y = the tens digit.
The number looks like yx.
The value of the original number is
10y + x
"the difference in the units digit and the tens digit is 5."
x - y = 5 Equation 1
When you reverse the digits, you have xy.
The value of the new number is
10x + y
"If the digits are reversed, the new number is the sum of twice the original number and seven."
10x + y = 2(10y + x) + 7 Equation 2
We have a system of 2 equations.
x - y = 5
10x + y = 2(10y + x) + 7
Simplify the second equation.
10x + y = 2(10y + x) + 7
10x + y = 20y + 2x + 7
8x - 19y = 7
x - y = 5
8x - 19y = 7
Solve the first equation for x. Substitute that value for x in the second equation.
x = 5 + y
8(5 + y) - 19y = 7
40 + 8y - 19y = 7
-11y = -33
y = 3
x = 5 + y
x = 5 + 3
x = 8
The digits are:
ones digit: 8
tens digit: 3
The number is 38.