The larger of two numbers is 23 less than twice the smaller. If the sum of the two numbers is 70, how do you find the two numbers?

39, 31

Explanation:

Let $L$ & $S$ be the larger & smaller numbers respectively then

First condition:

$L = 2 S - 23$

$L - 2 S = - 23 \setminus \ldots \ldots \ldots . \left(1\right)$

Second condition:

$L + S = 70 \setminus \ldots \ldots . . \left(2\right)$

Subtracting (1) from (2), we get

$L + S - \left(L - 2 S\right) = 70 - \left(- 23\right)$

$3 S = 93$

$S = 31$

setting $S = 31$ in (1), we get

$L = 2 \left(31\right) - 23 = 39$

Hence, the larger number is $39$ & smaller number is $31$