The sum of two numbers is 17. One number is 3 less than #2/3# of the other number. What is the lesser number?

2 Answers
Apr 12, 2017

Let's write these as equations.

"The sum of two numbers is 17."

Calling these unknown numbers #x# and #y#, we can write that:

#x+y=17#

Then, we see that "one number is 3 less than 2/3 of the other number."

Let's say that #y# is the "one number." If #y# is 3 less than 2/3 of #x#, this is written as:

#y=2/3x-3#

From here, we have to take this equation for #y# and use it in our first equation. Since we know that #y# and #2/3x-3# are equal, we can replace #y# with #2/3x-3# in the first equation:

#x+color(blue)y=17#

#x+color(blue)(2/3x-3)=17#

From here, we can add #x+2/3x# using fractions: #x+2/3x=3/3x+2/3x=5/3x#

#5/3x-3=17#

Add #3# to both sides of the equation:

#5/3x=20#

Multiply both sides by #3/5#:

#x=20xx3/5=(5(4)(3))/5=12#

If #x=12#, then #y=5#, since their sum is #17#.

So the two numbers are #5# and #12#.

Apr 12, 2017

The smaller number is #5#

Explanation:

It is possible to define the two numbers using only one variable.

Let the smaller number be #x#

The other number is #(17-x)" "# (We know they add up to #17)#

#2/3# of the bigger number is written as: #2/3(17-x)#

The smaller number is #3# less than that. (so, subtract #3# to get #x#)

#x = 2/3(17-x)-3" "larr# we have an equation, solve for #x#

#3x = cancel3xx2/cancel3(17-x) -3xx3" "larr xx 3#

#" "3x =34-2x -9#
#3x+2x = 25#
#" "5x = 25#
#" "x =5#

The smaller number is #5#, the larger is #12#

Check: #2/3 xx 12 - 3 = 8-3 = 5#