# The sum of two numbers is 48. The difference of the same two numbers is 24. What are the numbers?

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• 12 and 36

Subtract them: 36 - 12 = 24 (difference)

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• x + y = 48

x - y = 24

x = 36, y = 12

The two numbers are 36 and 12.

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• Let's do some algebra.

We can express this as a quadratic, via taking the 4th root of unity of the difference between 48 and 24, which is 24.

Then, applying Vieta's Formulas, and phi(48)+phi(24) (phi is totient function), we get

x^2 - 48 x + 432 = 0

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• The numbers are 12 and 36.

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• x + y = 48

x - y = 24

---------------

2x = 72

solve for y from eq 1

x + y = 48

36 + y = 48

y = 48 - 36

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• x  + y   = 48

2x   = 72

x   = 36

y   = 12

Numbers are 12  and  36

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• The sum of two numbers is 48.

The difference of the same two numbers is 24.

x + y = 48

x - y = 24

x = 36, y = 12

The two numbers are 36 and 12.

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• x+y = 48

x-y  = 24

-----------

2x   = 72

x = 36, y = 12

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• Let a be the bigger number

Let b be the smaller number

a + b = 48

a - b = 24

2a = 72

a = 72/2

a = 36

Then plug that into either equation to figure out b:

36 + b = 48

b = 48 - 36

b = 12

36 and 12

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• a + b = 48

a – b = 24

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