One number added to three times another number is 24. Five times the first number added to three times the other number is 36. Find the numbers.
The numbers are 3 and 7
Let the first number be "x"
Let the other number be "y"
Given that One number added to three times another number is 24
first number + three times another number = 24
x + 3y = 24 ------- eqn 1
Also given that Five times the first number added to three times the other number is 36
Five times the first number + three times the other number = 36
5x + 3y = 36 ------ eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
x = 24 - 3y ----- eqn 3
Substitute eqn 3 in eqn 2
5(24 - 3y) + 3y = 36
120 - 15y + 3y = 36
120 - 12y = 36
12y = 120 - 36
12y = 84
From eqn 3,
x = 24 - 3(7)
x = 24 - 21
Thus the numbers are 3 and 7
