Answer: The numbers are 74 and 47
Step-by-step explanation: X and Y represent the digits. A digit in the Tens place has 10 times its base value. So we can set up equations to model the information given:
10x+y = 10y + x +27
X + Y = 11
y =11-x Rewritten to substitute for y in the first equation.
10x + 11-x = 10(11-x)+x +27 Distribute and then combine like terms.
10x -x +11 = 110 -10x +x
9x + 11 = 110 +27 - 9x Add 9x to both sides and subtract 11 from both sides.
9x +9x = 110 + 27 - 11 Combine like terms:
18x = 126 Divide both sides by 18
x = 7
7 +y= 11 Substitute 7 for x to solve for y.
y= 4
Substitute the values of x and Y into the original equation.
70 +4 = 40 +7 + 27 Combine
The numbers look like 74 and 47.
Check:
74 = 47 + 27 Add 47+27
74 = 74
True!
