# COMPARING PROPORTIONAL AND NONPROPORTIONAL SITUATIONS

We can use what we have learned about proportional and non-proportional relationships to compare similar real-world situations that are given using different representations.

Example 1 :

A laser tag league has the choice of two arenas for a tournament. In both cases, x is the number of hours and y is the total charge. Compare and contrast these two situations. Solution :

Arena A :

Arena A’s equation has the form y = mx + b, where b = 0. So, Arena A’s charges are a proportional relationship. The hourly rate, \$225, is greater than Arena B’s, but there is no additional fee.

Arena A :

Arena B’s graph is a line that does not include the origin. So, Arena B’s charges are a non-proportional relationship. Arena B has a \$50 initial fee but its hourly rate, \$200, is lower.

Example 2 :

Jessika is remodeling and has the choice of two painters. In both cases, x is the number of hours and y is the total charge. Compare and contrast these two situations. Solution :

Painter A :

Painter A’s equation has the form y = mx + b, where b = 0. So, Painter A’ s charges are proportional. The hourly rate, \$45, is greater than Painter B’s, but there is no additional fee.

Painter B :

Painter B’s table is a nonproportional relationship because the ratio of y to x is not constant. Because the table contains the ordered pair (0, 20), Painter B charges an initial fee of \$20, but the hourly rate, \$35, is less than Painter A’s.

Example 3 :

Compare and contrast the following two situations.

 Test-Prep Center AThe cost for Test-Prep Center A is given by  c = 20h, where c is the cost in dollars and h is the number of hours you attend. Test-Prep Center BTest-Prep Center B charges \$25 per hour to attend, but you have a \$100 coupon that you can use to reduce the cost.

Solution :

Test-Prep Center B :

Test-Prep Center A is cheaper for greater than 20 hours;

Test-Prep Center B :

Test-Prep Center B is cheaper for less than 20 hours. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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Domain and range of rational functions

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Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

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Remainder when 17 power 23 is divided by 16

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Sum of all three four digit numbers formed with non zero digits

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