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

Lets x and y are 2 unknown numbers

3x=4y

x + y = 21 so x = 21 - y

replace x = 21 - y into 3x = 4y

3x = 4y

3 (21 - y) = 4y

63 - 3y = 4y

63 = 7y

y = 63/7

y = 9

x = 21 - y

x = 21-9

x = 12

answer

the numbers are 9 and 12

double check

sum of the numbers is 21 find the numbers = 9 + 12 = 21

Three times the larger of two numbers is equal to four times the smaller

3x=4y

3 (12) = 4 (9)

36 = 36