We have decided to sell laces for sports shoes. We will sell different lengths for shoes with different numbers of eyelets. We will offer lengths for sport shoes that have 4 eyelets all the way up to 18 eyelets (no odd numbers, of course). No one have ever sold so many different lengths for sports shoes before. You have to figure out what lengths to make and which lengths go with which shoes, based on the number of eyelets.
We collected some data from store customers last week. It is confusing because there haven’t been very many lengths available. That means that sometimes the customers have had to use lengths that are top short or too long. That’s not what we want! We want a unique length for each number of eyelets.
DATA FROM STORE CUSTOMERS WITH SPORTS SHOES Customer Lace Length Eyelets | Customer Lace Length Eyelets I.D. (inches) (numbers)| I.D. (inches) (numbers) | A 45 8 | G 54 12 B 54 10 | H 24 4 C 26 4 | I 72 14 D 63 14 | J 54 12 E 63 12 | K 72 16 F 36 8 | L 72 18
Write your decisions about lace length so the advertising people making the sign can understand it. They want a table, so customers can look up the number of eyelets and find out the length of lace. They also want a rule, so customers who don’t like tables can use the rule to figure out the lengths. Don’t worry about making it pretty, they will do that, just make sure the mathematics is right. You better explain how your decisions make sense so the advertising people will understand.
Thanks,
YOUR BOSS,
Angela
The rule: 3(e-1) + 20 = x e = number of eyelets x = length of lace The TableEyelets Length of lace 4 29 inches 6 35 inches 8 41 inches 10 47 inches 12 53 inches 14 59 inches 16 65 inches 18 71 inches
“The length of each lace allows enough for 3 inches between each eyelet, plus 20 inches for the bow. Of course, many people use more than 20 inches for their bow, but most don’t use a whole 3 inches for each eyelet, so there should be plenty. The table also pretty much corresponds with the data from the customers. The role of thumb I did will always tell the exact length needed.”
