The sum of two numbers if 67. the smaller number is 3 less than the larger number. what are the 2 numbers?

2 Answers
Serena D.
Jan 19, 2018

Set up a system of equations.

Explanation:

I am going to use x for the smaller number and y for the larger one.

The sum of both these numbers is 67, so the equation should be:
#x+y=67#

Since the smaller number is three less than the larger number, that means 3 has to be added to the smaller number to make it equal in size to the larger number.
#x+3=y#

To solve the equation, simply plug in #x+3# for the y variable in the first equation.

#x+x+3=67 rarr# Rewrite the first equation

#2x=64 rarr# Subtract 3 from each side, combine like terms

#x=32 rarr# Divide each side by 2

The smaller number is 32, so we plug that in to the second equation to find the larger number.

#32+3=y#

#y=35#

The two numbers are 32 and 35

Rachel
Jan 19, 2018

#35# and #32#

Explanation:

Let's say #x < y#

#x+y=67#

#x=y-3#

#:.#

#y-3+x67#

#2x-3=67#

#2y=70#

#y=35#

Now we solve for #x#

#x+35=67#

#x=32#

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