To Whom It May Concer:

This word problem is driving me nuts! I could really use your help. Its a secondary level question. Here it is:

A group of students planned to charter a bus for a school field trip. Each student was to share the $810 cost equally. However, 3 people were unable to go and this increased the share of each person by $3. How many went on the trip?

Thanks!

Hi again Jennifer,

As in the last problem you sent us the approach is to describe the problem in terms of equations and then use the mathematics you know to solve the equations. In this problem the statement "Each student was to share the $810 cost equally." means that if you multiply the number of students by the price each student is to pay you get the total cost of $810. To write this as an equation you need a variable to represent the number of students and another to represent the amount each student will pay so let n be the number of students and $p the amount each student will pay. Then

The next statement "However, 3 people were unable to go and this increased the share of each person by $3." says that if there are n - 3 people then they each have to pay p + 3 dollars to cover the &810 cost. That is

If you expand the left side of this equation and use the fact that n p = $810 you should be able to conclude that p = n - 3. If you now use this conclusion to replace p by n - 3 in the first equation you will get a quadratic that you can solve for n.

Cheers
Jack and Penny