Word problem

Question

Mr.chan buys some pencils for a group of students. If he gives them 2 pencils each, he will have 10 pencils left. If he gives them 3 pencils each, he will have none left. How many students are in the group?

Answer 1

Let's say that the number of students in Mr. Chan's class is x and the total Number of pencils that he has is T.

 

The second sentence says that each student gets two pencils and Mr. Chan has 10 left over. We need to make a mathematical equation for that.

 

2*x + 10 = T

 

2*x because each student gets two pencils, and +10 because he has ten left over.

 

We need to convert the third sentence in a similar manner. It says that is he gives three pencils to each student, he will have none left.

 

3*x + 0 = T

 

Now, both equations are equal to the same total, T. If they're both equal to the same thing, than we can set the equations equal to each other.

 

2x + 10 = 3x

 

Now, solve for x like you would in any other math problem - group like terms and then simplify. I see that there are more x's on the right than on the left, so I will aim to get all the x's on the right.

 

Subtract 2x from both sides to get:

 

10 = 3x - 2x

 

10 = 1x

 

10 = x

 

So, we found out that x=10. What was x, again? It was the number of students in Mr. Chan's class.

 

To verify, let's plug it in and see what happens.

 

2 * 10 + 10 = 30 pencils

 

3 * 10 = 30 pencils

 

So, we're now confident that this is the solution. I hope this helps!