How do I set this up as an inequality?

Question

Amy's final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs more than 84 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.

Answer 1

This problem is telling you that Amy's total score needs to be above 84. We need to find a way to represent Amy's score. She's getting points from true/false and multiple choice questions, so her score is:

 

true/false points + multiple choice points = Amy's score

 

She gets 3 points for each true/false she gets correct means true/false points = 3x

She gets 4 points for each multiple choice she gets correct means multiple choice points = 4y

 

So Amy's score is:

 

3x + 4y = Amy's score

 

 

The inequality comes in when we are told she needs "more than 84 points" on her test.

 

Amy's score > 84

 

So we use our equation from above to represent Amy's score:

 

3x + 4y > 84

 

I hope that helps! Let me know if you would like more of an explanation.

Answer 2

The way to tackle this problem, or any word problem for that matter, is to glean all the mathematically pertinant information out of it. We've got true/false questions, x, worth 3 points each, and MC questions, y, worth 4. That means every correct T/F gets multiplied by 3, or 3x. Same with the MC; 4y. She needs her score to be GREATER THAN, or > (as opposed to 'at least' which would imply greater than or equal to, or 'exactly' which would imply =) 84 points. 

 

So her total number of points (the SUM of our 3x and our 4y) must be GREATER THAN 84. Put it all together and you have your answer! 

 

Good luck!