Answer: The numbers are 56 and 36
Step-by-step explanation: The first thing is to assign letters to the two unknown variables. The first number shall be called a and the other one shall be called b.
If the sum of two numbers is 92, then
a + b = 92. This is our first equation.
If their difference is twenty, then
a - b = 20. This is our second equation.
Now what we have here is a pair of simultaneous equations as follows
a + b = 92 —————(1)
a - b = 20 —————(2)
From equation (1) we can make a the subject of the equation
a = 92 - b
Substitute for the value of a in equation (2)
a - b = 20 now becomes
(92 - b) -b = 20
92 - b - b = 20
92 - 2b = 20
By collecting like terms we now have
92 - 20 = 2b
(Note that when a negative number crosses to the other side of an equation it becomes positive and vice versa)
92 - 20 = 2b
72 = 2b
Divide both sides of the equation by 2
36 = b
If b is 36, then substitute for the value of b in equation (1)
a + b = 92
a + 36 = 92
Subtract 36 from both sides of the equation
a + 36 - 36 = 92 - 36
a = 56
The numbers therefore are 56 and 36
