problem:the larger of two numbers is five more than twice the smaller number.the sum of the two numbers is 39.find the numbers.what is the equation  

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kjcdb8er | Teacher | (Level 1) Associate Educator

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Let the two numbers be x and y. x is smaller.

"two times the smaller number" is 2x

"five more than 2x" is 2x + 5 = "the larger number," y

So 2x + 5 = y            (1)

Also, x + y = 39         (2)

 

Multiply (2) by 2 so now you have:

2x + 5 = y

2x + 2y = 78

 

Subtract the two equations:

2x + 5 - (2x + 2y) = y - 78

5 - 2y = y - 78

3y = 83

y = 83/3

 

So x + y = 39  --> x = 39 - y = 39*3/3 - 83/3

x = 34/3

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