Three times the larger of two numbers is equal to four times the smaller. the sum of the numbers is 21 find the numbers

Define x :

Let x be the smaller number.
Let y be the larger number.


Construct the equations :

Three times the larger number is equal to 4 times the smaller ones.
⇒ 3y = 4x

The sum of the numbers is 21
⇒ x + y = 21


Solve for x and y :

3y = 4x (1)
x + y = 21 (2)


From equation (2) :

x + y = 21
x = 21 - y


Substitute x = 21 - y into equation (1) :

4y = 3( 21 - y)
4y = 63 - 3y
7y = 63
y = 9


Substitute y = 9 into equation 2 :

x + y = 21
x + 9 = 21
x = 21 - 9
x = 12


Answer : The two numbers are 9 and 12.