three times a number is subtracted from another number and the difference is 3. the sum of the two numbers is 31. What is the smaller of the two numbers

Question

An Answer would be great

Answer 1

Let x = the first number and y = the second number. We can form the following system of linear equations

 

y - 3x = 3

x + y = 31

 

Solve the top equation for y.

 

y = 3x + 3

 

Substitute this into the second equation

 

x + (3x + 3) = 31

 

4x + 3 = 31

 

4x = 28

 

x = 7

 

Since the sum of the two numbers is 31, it is obvious that x = 7 is the smaller of the two numbers