Question #73666

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Answer 1 · 2017-02-21T03:36:46

The larger number is 59.
The smaller number is 24

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

That means $L = 2S + 11$ .

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

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

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

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

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 $L$ ;
$L = 2S + 11$
$L = 2(24) + 11$
$L = 59$

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