#### A Math Forum Project

 ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary

Student Version

### Shoelaces 3 - posted March 27, 2000

Try Shoelaces 1 and Shoelaces 2 before you do this problem.
In this simulation you will learn about y-intercept and what it represents.

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Most submissions were correct, and two solution methods were used. Some students used the graph by lining up the appropriate lines and looking at the y-intercept. Others did the computations. There were some arithmetic errors (be careful out there!), and some solutions were submitted without explanations for how students found the answers.

The bonus seemed to be harder, or perhaps was not worded clearly. We were looking for the equation for the two solution lines that were found. Some people only gave equations for the other lines, and some were confused about what the equation should look like, but some got it right, too.

### Highlighted solutions:

 From: Andy E., age 13Vasiliy S., age 13Tyler M., age 14 School: Issaquah Middle School, Issaquah, WA

```Page Manipulating the Y-Intercept

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.

------------------------------------
```

 From: Allison C., age 12Justine W., age 12 School: Issaquah Middle School, Issaquah, WA

```Page Manipulating the Y-Intercept

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?
We want to ask for \$150 as a base pay.  Since we want the same pay after
selling 50 pairs of shoes as the person who has no base pay but gets \$5/pair,
we adjusted the green line on the graph so it intersects with the red line
where the x axis is 50.  When that was done, we found the y-intercept of the
green line and it was \$150.

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?
We would ask for a base pay of \$262.50.  Since we want the same pay after
selling 25 pairs of shoes as the person who gets a \$300 base pay and earns
\$.50 for each pair of shoes they sell, so we adjusted the green line so it
intersects with the blue line (which represents the person whose salary we are
trying to equal) where the x axis is 25.  When that was done, we found the y-
intercept of the green line and it was \$262.50.

Bonus: Write the equations of the two lines you used to answer questions 1 and
2. Explain the elements of the equations.
red line
y=5x
y is the number on the y axis (weekly salary), and x is the   number on
the x axis (the # of pairs of shoes)
blue line
y=0.5x +300
300 is the base pay, y is the weekly salary, and x is the number of pairs
of shoes.
------------------------------------
```

### 38 students received credit this week.

Jared A., age - Issaquah Middle School, Issaquah, WA
Amy B., age 13 - Issaquah Middle School, Issaquah, WA
Andrea B., age - Issaquah Middle School, Issaquah, WA
Brooke B., age 14 - Issaquah Middle School, Issaquah, WA
Hana B., age - Issaquah Middle School, Issaquah, WA
Steven B., age 14 - Issaquah Middle School, Issaquah, WA
Allison C., age 12 - Issaquah Middle School, Issaquah, WA
Marshall C., age - Issaquah Middle School, Issaquah, WA
Sarah C., age 13 - Issaquah Middle School, Issaquah, WA
Andrew D., age 14 - Issaquah Middle School, Issaquah, WA
Cameron D., age - Issaquah Middle School, Issaquah, WA
Ellie D., age 14 - Issaquah Middle School, Issaquah, WA
Katie D., age 13 - Issaquah Middle School, Issaquah, WA
Megahn D., age 13 - Issaquah Middle School, Issaquah, WA
Andy E., age 13 - Issaquah Middle School, Issaquah, WA
Greg H., age 12 - Issaquah Middle School, Issaquah, WA
Chris I., age 13 - Issaquah Middle School, Issaquah, WA
Katelyn J., age 13 - Issaquah Middle School, Issaquah, WA
Arthur K., age - Issaquah Middle School, Issaquah, WA
Brian L., age 13 - Issaquah Middle School, Issaquah, WA
Bryan L., age 13 - Issaquah Middle School, Issaquah, WA
Chris L., age 13 - Issaquah Middle School, Issaquah, WA
Daniel L., age - Issaquah Middle School, Issaquah, WA
David L., age 13 - Issaquah Middle School, Issaquah, WA
Derek L., age 13 - Issaquah Middle School, Issaquah, WA
Robert M., age 13 - Issaquah Middle School, Issaquah, WA
Tyler M., age 14 - Issaquah Middle School, Issaquah, WA
Chris N., age 13 - Issaquah Middle School, Issaquah, WA
Cassie R., age 13 - Issaquah Middle School, Issaquah, WA
Jamin S., age 13 - Issaquah Middle School, Issaquah, WA
Paradie S., age - Issaquah Middle School, Issaquah, WA
Vasiliy S., age 13 - Issaquah Middle School, Issaquah, WA
Sei T., age 12 - Issaquah Middle School, Issaquah, WA
Andrew W., age 13 - Issaquah Middle School, Issaquah, WA
Benjamin W., age 14 - Issaquah Middle School, Issaquah, WA
Justine W., age 12 - Issaquah Middle School, Issaquah, WA
Brian Y., age 14 - Issaquah Middle School, Issaquah, WA
Devon Y., age - Issaquah Middle School, Issaquah, WA