# Question #73666

Feb 21, 2017

The larger number is 59.
The smaller number is 24

#### Explanation:

The larger number $L$ is $11$ more or $+ 11$ than twice the smaller $S$ number or $2 \times S$.

That means $L = 2 S + 11$.

Now $3$ times the larger or $3 \times L$ is $9$ more or $+ 9$ than $7$ times the smaller or $7 S$.

That means $3 L = 7 S + 9$.

We can multiply both sides of the first equation by $3$ so it will match the second equation for the $L$ term.
$3 L = 6 S + 33$

We can now substitute the value of $3 L$ into the second equation:
$6 S + 33 = 7 S + 9$

Subtract $S$ values from the right side and number values from the right side to bring them across the $=$ sign.
$- S = - 24$
$S = 24$

Using the first equation to solve for $L$;
$L = 2 S + 11$
$L = 2 \left(24\right) + 11$
$L = 59$

To check, substitute the values back into the second equation:
$3 L = 6 S + 9$
$177 = 168 + 9$
$177 = 177$