help!

 

The sum of two numbers is 37. The greater number is 5 more than three times the lesser number. What is the lesser of the two numbers?   

 

Call the lesser number X 

Call the greater number Y 

 

given                                 X + Y = 37     which means that Y = 37 – X   substitute this for the Y In the next given equation

given                                 Y = 3X + 5

 

                                          37 – X = 3X + 5   

add X to both sides            37       = 4x + 5 

subtract 5 from both sides       32 = 4X  

divide both sides by 4                8 = X      the lesser number is 8  

 

by the way, X + Y = 37 which means that the greater number is 29 but the problem didn't ask for that.

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x = lesser number      other number  = 5 + 3x    sum to 37

x   +   5+3x = 37

4x = 32

x = 8 = lesser number