inequality word problem

Question

Eddie scored at least 27 points more than half of what Duncan scored.
Eddie scored 58 points. Write an inequality that could be solved to find
the numbers of points that Duncan could have scored.

Answer 1

This problem is asking you to write an inequality and solve it in the same way you would solve an algebraic equation.

 

Let x = Duncan's score.

We know that whatever Duncan scored, if you add at least 27 points to half of it, it would be at least 58, meaning the sum could be exactly 58, or it could be greater.

 

Your inequality should look like this:

1/2x + 27 ≥ 58

 

We solve this the same way that we would solve an equation, using the reverse order of operations (or SADMEP) to isolate the variable and find its value.  Remember that whatever you do to one side of the inequality, you have to do to the other.

 

The first step would be to subtract 27 from both sides:

1/2x + 27 ≥ 58

         - 27   -27

 

The 27's on the left cancel out and we're left with:

 

1/2x ≥ 31

 

Next we divide by 1/2.  Remember that dividing by a fraction is the same as multiplying by its reciprocal.  So essentially, we are multiplying both sides of the inequality by 2. Here's what we're left with.

 

x ≥ 62

 

Because "x" is or is greater than 62, we know that Duncan scored at least 62 points.  You can check this answer by plugging 62 back into your original inequality  and seeing if it makes sense.

 

Hope this helps :)