Question #73666

1 Answer
Feb 21, 2017

Answer:

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 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#