Question

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

Answer 1

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

Answer 2

`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`