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Algebra
Question

The sum of two numbers is \( 92 \) . The differenc...

The sum of two numbers is \( 92 \) . The difference of the two numbers is \( 44 \) . What are the two numbers. Let \( x \) be the larger number and \( y \) be the smaller number. Write an equation that expresses the information in the sentence "The sum of two numbers is \( 92 \) ." 

 

Write an equation that expresses the information in the sentence "The difference of the two numbers is 44."" 

 

Solve the system you have written above.

 

The larger number, \( x \) is \( \square \) . The smaller number, \( y \) is \( \square\) 

Answer

The sum of two numbers is 92.                   \(x+ y = 92\)

The difference of two numbers is 44.          \(x- y = 44\)

Adding these two equations, we get           \(2x = 136 ~~\Rightarrow~~ x = 68\)

Subtracting these two equations to get       \(2y = 48 ~~\Rightarrow~~ y = 24\)

Larger number is x = 68 and smaller number is y = 24

Solution
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