The sum of two numbers is 130 and their difference is 54. What are the two numbers?

Question

The sum of two numbers is 130 and their difference is 54. What are the two numbers?

Answer 1

Hi Adam, set this up as a system of equations. Let x represent one number and y represent the other one.

Equation 1, sum of the numbers:

x + y = 130

Equation 2, difference of the numbers:

x - y = 54

System of equations to solve:

x + y = 130

x - y = 54

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Add the two equations to eliminate the y term leaving:

2x = 184

Divide by 2:

x = 92

Find y from first equation:

92 + y = 130

Subtract 92 from both sides:

y = 38

Answer:

The two numbers are 92 and 38.

Questions?

Answer 2

x + y = 130

x - y = 54

Sum these:

2x = 184

x = 92

y = 38