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The numbers are 1 and 18
<em><u>Solution:</u></em>
Let the smaller number be "x"
Let the larger number be "y"
Given that smaller of two numbers is five less than the larger number
smaller number = one - third of larger number - 5
3x = y - 15
y = 3x + 15 ------- eqn 1
Half the larger added to the smaller is 10
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
<h3>x = 1</h3>From eqn 1,
y = 3(1) + 15 = 18
<h3>y = 18</h3>Thus the numbers are 1 and 18