# Got Lanyards?

## Part I

Coppell Middle School West wants lanyards for school ID's! They spoke with Bart's Neck Pieces and chose me to figure out what scheme is the most affordable! Listed below are their schemes:

1. \$35 for the first lanyard, \$5 for each additional

2. \$65 for the first lanyard, \$3 for each additional

3. \$95 for the first lanyard, \$1 for each addiotional

## Which One is Best?

I chose one number to test the schemes: 10 lanyards

I plugged them into the equation and figured out what the total cost would be.

Here are my results.

Scheme 1:

35+5x=y As you can see, when 10 lanyards are

x=9 ordered, the most affordable

35+5x9=y scheme is the first one.

35+45=y

80=y

Scheme 2:

65+3x=y

x=9

65+3x9=y

65+27=y

92=y

Scheme 3:

95+x=y

x=9

95+9=y

104=y

Results:

As you can see, when 10 lanyards are

ordered, the most affordable

scheme is the first one.

## Part II

Already, 50 students have ordered their lanyards! We need to find out which deal will be best for them.

Scheme 1:

35+5x=y

x=49

35+49x5=y

35+245=y

280=y

Scheme 2:

65+3x=y

x=49

65+3x49=y

65+147=y

212=y

Scheme 3:

95+x=y

x=49

95+49=y

144=y

## Part III

The school has now requested that we purchase \$500 worth of lanyards.

Scheme 1:

35+5x <_ 500

5x<_465

x<_93

The amount we could buy from Offer 1 is 93 or more.

Scheme 2:

65+3x<_500

3x<_435

x<_145

The amount we can buy from Offer 2 is 145 or more.

Scheme 3:

95+x<_500

x<_405

The most we could but from Offer 3 is 405 or more.

## All in all.....

The best possible option is the third one because even though the flat fee is \$95, the cost of the additional lanyards was only one dollar. Even though for 10 lanyards, option 1 is best, when buying in bulk, option 3 is best.