The sum of two numbers is 27. The larger number is 6 more than twice the smaller number. What are the numbers?

2 Answers
May 6, 2017

Answer:

#7# and #20#.

Explanation:

Okay, I'm going to put these as an equation, to make things a bit easier for you.

Let #x# be the bigger number and let #y# be the smaller number.

#x + y = 27#

#x = 2y +6#

Once you see those, it's quite clear that this is a simple substitution problem. So, let's solve for #y# first:

#2y+6+y=27#

And then let's substitute it in for the first number:

#3y +6-6=27-6 #

#3y= 21#

#y=7#

And then to solve for #x#:

#x +7=27#

#x+7-7=27-7#

#x=20#

May 6, 2017

Answer:

The smaller number is #7#, the larger is #20#

Explanation:

This problem can be solved using just one variable.

Let the smaller number be #x#.

If the two numbers add to 27, then the numbers can be written as:

#x and (27-x)#

Twice the small number: #2x#
Six more than twice the smaller number: #2x +6#

That is the same as (=) the bigger number:

#2x+6 = 27-x#

#2x+x = 27-6#

#3x = 21#

#x =7#

If the smaller number is #7#, the larger is #20#

Check: #2 xx 7 +6 = 20#