## Monday, November 25, 2013

### Lines Problem Three

This problem comparing two types of gym memberships — one with an up-front fee and a monthly fee and the other with just a monthly fee was motivated by a video at Khan Academy.

It should be useful for teachers and parents to follow up Khan videos with problems related to the video.

Question:   A gym offers two type of memberships.  The first membership has a \$200 up-front fee and a \$40 a monthly charge.   The second membership has a \$50 up-front fee and a \$70 monthly charge.   How many months must a person be a member of the gym in order for the first membership to be less expensive than the second membership?

Answer:  M is the number of months the person is a member of the gym.  The person is indifferent to the two memberships if

\$200+\$40M = \$50+ \$70M

Rearrange we get

\$150 = \$30 M

or M=5.

when M= 5 the total amount of money spent on the gym  membership is \$400 under both payment plans.

When M=4 the total expenditure on the first plan (with the \$200 upfront fee) is \$360.  It exceeds cost of the second plan, \$330.

For M=6 expenditures are \$440 for the first plan and \$470 for the second plan.

Go here for more problems on lines:

http://www.dailymathproblem.com/p/questions-on-lines.html