This math problem shows our technique for explaining with colored "motion lines" and clear answers. When you read the chat, you will immediately notice that the student leads the discussion rather that the tutor or teacher quizzing the student.

All students have different questions arising from their unique perspective. When a student is able to ask as many questions as he or she needs to understand, the student is finally able to master for the first time the math concepts that initially seem so hard.

Tom bought 25 candies for 19 dollars. He only bought candies worth 1 dollar or 50 cents. How many one-dollar candies did he buy? How many fifty-cents candies did he buy?

Tutor: Hi! I am now working on your question and you will soon see me writing on your drawing board.
Student: Okay. Thank you.
Tutor: First, let's set the variables.
Student: Ok
Tutor: We will make "x" be the amount of 1 dollar candies and "y" the amount of 50 cents candies.
Tutor: So x plus y must be 25.
Student: But how do we solve for x?
Tutor: Not possible yet. We first need a second equation because we have 2 variables.
Student: Ok. What is the second equation?
Tutor: To do this, we will use the information from the cost of the candies.
Tutor: We know that Tom bought x candies for $1.00 and y candies for $0.50. This means 1x + 0.5y = 19.
Student: That was tricky but I see what you did.
Tutor: Now we are ready to solve a problem with two equations using the eliminate method. We do this by subtracting the second equation from the first.
Student: Ok.I see what you did. I can do that now.
Tutor: Excellent. Now we need to solve for x.
Student: I get that part. We substitute back into the first x+y=25 equation.
Tutor: Exactly. I'll do that quickly and you can see that x=13.
Student: You mean 13 one dollar candies?
Tutor: That's right :)
Tutor: Are there any more questions that I can help you with?
Student: Thank you! That's all!
Tutor: Thank you for using 24/7 Math Help.
Student: Bye!
Tutor: Good bye!
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