The Magic of Proportions

My daughter loves to watch the CSI and NCIS programs (all of them) and is fascinated with the idea of being a crime scene investigator.  As we talked last night, she pointed out that the CSI investigators, as part of their investigation for the recent shooting at Fort Hood, would have to draw the crime scene as documentation of physical evidence locations, as well as measurements showing pertinent size and distance relationships in the crime scene area.  So, if the area of the shooting was 50 ft x 60 ft, how large of a piece of a paper would they need to use if the scale was 1in:5ft?

For this you would first need to set up two proportions and solve:    

1 in/5 ft = x in/50 ft 

50 in/5 = x in 

10 in = x                                 

and                 

1 in/5 ft = x in/60 ft

60 in/5 = x in

12 in = x

The steps used to solve both of the proportions are:

1.  Multiply both sides of the proportion by the amount of the denominator where x is the numerator (multiplicative identity property)

2.  Reduce the resulting fraction to simplest form (divide the numerator by the denominator).

The CSI investigator will need a sheet of paper that is at least 10” by 12” to draw the crime scene for the investigation.  I would add a one inch border, so the paper size would need to be 11″ by 13″.

Every year the youth group at my church conducts a spaghetti dinner fundraiser.  Last year, the youth made 20 batches of homemade spaghetti sauce and served 140 people.  This year, the group has already sold 200 dinner tickets.  They also feel that they will have approximately 40 people who will buy tickets at the door.  They are now trying to determine how many batches of spaghetti sauce they will need to make to serve 240 people.

First you would need to set up one proportion: 

20 batches/140 people = x batches/240 people

4800 batches/140

34.29 batches = x

To solve the proportion:

1.  Multiply both sides by the denominator where x is the numerator (240).

2.  Simplify the resulting fraction by dividing the numerator by the denominator.

In order to be sure that all 240 people can be served, the youth group will need to make 35 batches of spaghetti sauce.  WOW, that is a lot of sauce!

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