The difference between two numbers is 5. 6 less than twice the smaller number is the larger number. What are the numbers?

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Answer 1 · 2018-03-26T00:37:58

The two numbers are 16 and 11.

Let's call the two numbers #x# and #y#.

According to the question, the difference between the two numbers is 5, so:

#x-y=5#

In this case, the difference is a positive number, so that means #y# is smaller than #x#.

The next statement is "6 less than twice the smaller number is the larger number". Let's express this as an equation:

#2y-6=x#

Now we have a system of two equations. Let's add the two equations together:

#(x-y)+(2y-6)=(5)+(x)#

#rArrx+y-6=5+x#

Now we can eliminate #x# and solve for #y#.

#rArrcancelx-color(red)cancelx+y-6=5+cancelx-color(red)cancelx#

#rArry-6=5#

#rArry-cancel6+color(red)cancel6=5+color(red)6#

#rArry=11#

Now that we know #y#, we can substitute it into our first equation:

#x-y=5#

#rArrx-11=5#

#rArrx-cancel11+color(red)cancel11=5+color(red)11#

#rArrx=16#

Let's check that our equations both hold true for
#x=16# and #y=11#:

#16-11=5#
#5=5#
Check!

#2(11)-6=16#
#22-6=16#
#16=16#
Check!