Shoelaces 3
posted March 27, 2000 as a Math Forum EPoW

Introduction: In this problem, students use graphing skills to help store customers choose the best shoelace length and giftwrappers the best ribbon length.

Where's the Math: The problem series encourages students to make predictions and develop generalizations from data represented on a graph. In this part of the series, students explore issues of scale and the meaning of y-intercepts. Standards: Data analysis and probability, measurement, algebra Role of Components: The Shoelaces problem uses the PEN component overlayed on top of a SimCalc graph to provide scafolding to students new to point plotting. Positive feedback is given in the form of a green circle that appears on the graph when the student moves the mouse over a point in a given list. The second part of the EPoW used PEN with simple function to fit a line to the set of plotted points. Students experiment with the y-intercept using a swing slider. Graph instructions are displayed via the HTML viewer, and solutions are entered in a text entry box. Javascript handles communication among components.

(The applet for this problem is currently unavailable) 

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Sample submitted solution:

From: Andy, age 13
Tyler, age 14
Vasiliy, age 13
School: Issaquah Middle School, Issaquah, Washington

1. You need to figure out what base pay you should ask for, knowing that: a. you can sell 50 pairs of shoes in a week, b. you will earn $2 commission on each pair you sell, and c. you want to earn the same full salary as someone who gets no base pay and earns $5 per pair (red line). What base pay would you ask for? How did you figure it out?
The Base Pay i'd ask for is $150. By using the graph you see that if you have no base pay you make $100 from the commission of shoes alone at $2 per shoe, and you make $250 from commission of shoe sales when you get $5 per pair of shoes sold, and $250-$100 gives you the weekly salary.

2. This time figure out what base salary you should ask for, knowing that: a. you can sell 25 pairs of shoes in a week, b. you will earn $2 commission on each pair you sell, and c. you want to earn the same full salary as someone who gets a $300 base pay and earns $.50 per pair (blue line). What base pay would you ask for? How did you figure it out?
$312.50-$50 = Base Salary for you Base Salary = $262.50

Bonus: Write the equations of the two lines you used to answer questions 1 and 2. Explain the elements of the equations.

 (No answer submitted)

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