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
Let's write these as equations.
"The sum of two numbers is 17."
Calling these unknown numbers
#x+y=17#
Then, we see that "one number is 3 less than 2/3 of the other number."
Let's say that
#y=2/3x-3#
From here, we have to take this equation for
#x+color(blue)y=17#
#x+color(blue)(2/3x-3)=17#
From here, we can add
#5/3x-3=17#
Add
#5/3x=20#
Multiply both sides by
#x=20xx3/5=(5(4)(3))/5=12#
If
So the two numbers are
The smaller number is
Explanation:
It is possible to define the two numbers using only one variable.
Let the smaller number be
The other number is
The smaller number is
The smaller number is
Check: