The sum of two numbers is 92. Their difference is twenty. Find the numbers

36 and 56

Step-by-step explanation:

check

36+56=92

56-26=20

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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

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