What two numbers have a sum of 24 and have a quotient of 3?

1st number is x
then the other will be 3x
3x+x=24
4x=24
x=6-first number
2nd is 3*6=18

Define x and y :

Let one number be x.
Let the other number be y.


Construct equation :

x + y = 24
x ÷ y = 3


Solve for x and y :

x + y = 24 (1)
x ÷ y = 3 (2)


From equation 1 :

x + y = 24
x = 24 - y 


Sub x = 24 - y into 2 :

x ÷ y = 3               // Equation 2
(24 - y) ÷ y = 3      // Sub x = 24
24 - y = 3y            // Multiply by y on both sides
24 = 4y                 // Add y to both sides
4y = 24                 // Switch side, make y the subject
y = 6                     // Divide by 4 on both sides


Sub y = 6 into equation 1 :

x + y = 24            // Equation 1
x + 6 = 24            // sub y = 6
x = 18                  // Take away 6 from both sides


Find the two numbers :

One number = x = 18
The one number = y = 6


The two numbers are 18 and 6.