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?

Question

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?

Answer 1

"The sum of two numbers is 37.":        

a+b=37

 

"The greater number [for us, let's say our greater number is b] is 5 more than [+] three times [*] the lesser number.":

b=5+3a

 

"What is the lesser of the two numbers?" We can find this by solving our system of equations:

 

a+b=37

b=5+3a  Let's rearrange this equation so a and b are on the same side of the equal sign.

-3a+b=5

 

Now let's subtract our two equations

 

       a+b=37

- [-3a+b=  5]

     4a+0=32

 

Now, we can solve for a. (We already said b was the greater number, so that means a is the lesser number.)

 

4a=32

  a=8

 

"What is the lesser of the two numbers?" 

Answer: 8