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Patterns, Functions, and Algebra
Session 4 Part A Part B Part C Part D Homework
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Session 4 Materials:



Solutions for Session 4, Homework

See solutions for Problems: H1 | H2 | H3

Problem H1

Chris's method will produce tea that has too much mix. This method would work only if the original recipe called for the same amount of tea and water, which it doesn't. In terms of fractions, 22/30 is not the same proportion as 12/20.


Pat's method is correct: 6/10 is the same proportion as 12/20, so the new mixture will have the right proportion of mix.


Sandy's method is also correct: 18/30 is the same proportion as 12/20.


Lee's method is identical to Chris's method. If you keep the difference between tea and water the same, there will be too much tea mix added at 30 cups.


Chris and Lee's suggestions are incorrect because they are absolute comparisons, where a relative comparison is needed to keep the proportion of tea mix the same.

<< back to Problem H1


Problem H2


The triangle with side lengths 6, 8, and 10 is similar looking. A good comparison is the measures of the three angles of the triangle.

<< back to Problem H2


Problem H3


The twins are Adam and David. We know they start at the starting line, so they must be the ones without any constants in their equations.


The oldest must be Eric, since he is the one whose equation includes the instruction "-5", which means he begins 5 meters behind the starting line.


Adam started at the starting line, and ran at 6 meters per second. Brett started 7 meters ahead, and ran at 4 meters per second.
Caleb started 4 meters ahead, and ran at 5 meters per second.
David started at the starting line, and ran at 5 meters per second.
Eric started 5 meters behind the starting line, and ran at 7 meters per second.


The points of intersection on the graph represent when one brother passes another during the race. Their times (on the horizontal axis) and their distance from the start (on the vertical axis) are the same.


Use t = 2 in all five equations, or refer to the graph. The order is: Brett (15 m), Caleb (14), Adam (12), David (10), and Eric (9).


Caleb and David, who run at the same speed. We know this because their graphs form parallel lines, which always stay the same distance apart.


Find the finishing times for the five by solving the equations for d = 30, or referring to the graph (draw a horizontal line at distance d = 30). Solving the equations shows that Adam and Eric tie for first (5 seconds), then Caleb (5.2), Brett (5.75), and David (6 seconds).


Adam and David. Their graphs pass through the origin (0, 0) and their equations are in the form y = kx.

<< back to Problem H3


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