The numbers are 1 and 18
Solution:
Let the smaller number be "x"
Let the larger number be "y"
Given that smaller of two numbers is five less than [tex]\frac{1}{3}[/tex] the larger number
smaller number = one - third of larger number - 5
[tex]x = \frac{1}{3} \times y - 5\\\\x = \frac{y - 15}{3}\\\\[/tex]
3x = y - 15
y = 3x + 15 ------- eqn 1
Half the larger added to the smaller is 10
[tex]\frac{1}{2}y + x = 10\\\\\frac{y + 2x}{2} = 10[/tex]
y + 2x = 20 ------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
3x + 15 + 2x = 20
5x = 20 - 15
5x = 5
From eqn 1,
y = 3(1) + 15 = 18
Thus the numbers are 1 and 18
