The sum of two numbers is 72, and twice their difference is 24. What is the smaller of the two numbers?
The smaller number is
Let's call the two numbers
The first sentence translates to
Since the difference is positive and
From this equation we can deduce
Substitute this expression for
We rearrange this equation as
and thus, dividing by
We wouldn't need
The smaller of the two numbers is 30.
To solve for one unknown, you need one equation. To solve for two unknown values, you need to set up two equations. To solve for three unknowns, you need three equations. In this case we have two unknowns.
First, you need to translate the given information into algebraic equations.
Let's call the unknown numbers
We are told that the sum of the two numbers is 72 so
That's one equation. We just need one more.
Twice their difference is 24.
Start with their difference
Twice this value is 24, so
Simplify this by dividing both sides by 2
Now that we have two the equations, you can use various methods such as substitution or elimination to solve. I will go with substitution.
From (2) we can rearrange it to get an expression of
Now substitute this expression into (1)
Simplify this and solve for
Now substitute this value back in to either (1) or (2) to solve for
As a final check you should test that the sum of the two numbers is 72 and that twice their difference is 24.