The sum of two numbers is 57, and the difference is 3.
Give each number a variable (as you do not know what they are): x , y
Set the equations:
"The sum of two numbers is 57": x + y = 57
"The(re) difference is 3": x - y = 3
Isolate one of the variables in the second equation. Add y to both sides:
x - y (+y) = 3 + y
x = 3 + y
Plug in "3 + y" for x in the first equation:
3 + y + y = 57
Simplify. First, combine like terms:
3 + (y + y) = 57
3 + 2y = 57
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS*.
*PEMDAS is the order of operation.
PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
First, subtract 3 from both sides:
2y + 3 = 57
2y + 3 (-3) = 57 (-3)
2y = 57 - 3
2y = 54
Next, divide 2 from both sides:
(2y)/2 = (54)/2
y = 54/2
y = 27
Plug in 27 for y in one of the equations:
x = 3 + y
x = 3 + (27)
x = 3 + 27
x = 30
x = 30 , y = 27 is your answer.
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Check:
"The sum of two numbers is 57": x + y = 57
30 + 27 = 57
57 = 57 (True)
"The(re) difference is 3": x - y = 3
30 - 27 = 3
3 = 3 (True)