Two friends Sheldon and Leonard decide to share an 18-inch sub using the divider

Question

Two friends Sheldon and Leonard decide to share an 18-inch sub using the divider-chooser method. As shown in the diagram, the leftmost third of the sub is meatball, the middle third is ham, and the rightmost third is vegetarian. The friends purchased the sub for $12.00 Meatball Ham Veggie 12 18 Sheldon does not like meatball subs and likes vegetarian subs three times as much as ham subs (a) How much (in dollars) is each portion of the sub worth to Sheldon? $ 0 $ 3 (meatball portion) (ham portion) (vegetarian portion) (b) They flip a coin and decide that Sheldon will be the divider. To split the sub, Sheldon will make a single cut perpendicular to the length of the sandwich Sheldon will cut the sub 4 x inches from the left. After Sheldon has cut the sub into two pieces, according to the divider-chooser method, Leonard will select one of these pieces. Leonard like vegetarian subs twice as much as meatball subs. He likes meatball and ham subs equally (c) How much (in dollars) is each piece worth to Leonard? (Note that the "pieces" in this part refer to the pieces created by Sheldon's cut. To complete this part of the problem you must first find the correct answer to part (b).) (left piece) (right piece) (d) Leonard will select the -Select- piece of the sub, leaving Sheldon with the other piece.

Explanation / Answer

Sheldon being the divider will try to cut the piece equally according to his own worth. He will make a cut 4 inches from right so that the left part consisting of meat ham and 2 inches of veggie makes a worth of $6 to him ( $3 is the worth of ham and $ 9 being the total worth of veggie for him 2 inch will worth $3 for him making $ 6 in toto) also the right part consisting of 4 inch of veggie wil with $ 6

Leonard worth will be $ 3 for meat $ 3 for ham and $ 6 for veggie as meat and ham both are equal for him as well as veggie is double of meat.

So left piece is of worth 3+3+2( 2 inch of veggie) for him that is $8

And right is $ 4 for him.

Obviously he will choose left part

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