By clue 4, lunch with Mr. Eakins went for twice as much as lunch with the
history teacher, whose lunch brought in $1 more than the lunch featuring a
peanut butter sandwich. By clue 8, the lunch with the roast beef sandwich
sold for twice as much as the lunch with the peach for a fruit. The roast
beef sandwich isn't on Mr. Eakins' or the history teacher's lunch menu (clue 12),
so the lunch it is in is the fourth one to the three in clue 4. Since no two
lunches sold for the same sum (intro) and Mr. Eakins isn't making the roast
beef sandwich, in clues 4 and 8, the peach isn't part of the history teacher's
lunch. The peach also isn't in Mr. Eakins' lunch and isn't in the same lunch
as the peanut butter sandwich (1), so the peach is in the fifth lunch
to the four already named. Then either the lunch with the peanut butter
sandwich or the one with the peach sold for the lowest amount, $6 (14). If
the peanut butter sandwich lunch had sold for $6, the history teacher's
lunch would have brought in $7 and Mr. Eakins' lunch $14 (4), a total of
$27, leaving $30 for the bids on the lunches in clue 8. Letting the lunch
with the peach being sold for X and the lunch with the roast beef then
2X (8), we would have 3X equal $30, or X = $10. The
lunch with the peach would have brought in $10 and the one with the roast
beef sandwich would have brought in $20. However, the only $3 range between
bids would be from the lunch with the peach to the history teacher'swhile
clue 6 requires that the math teacher's lunch go for $3 less than another
lunch. Therefore, the peanut butter sandwich lunch didn't go for $6; the
lunch with the peach as fruit did, and the one with the roast beef sandwich
sold for $12 (8)a total of $18, leaving $39 for the three lunches in clue
4. In clue 4, letting the lunch with the peanut butter sandwich sell for
X, the history teacher's lunch went for X+1 and Mr Eakins'
for 2X+2. Summing, we have 4X+3 equals 39, or X = 9.
The lunch with the peanut butter sandwich brought in $9, the history teacher's
sold for $10, and Mr. Eakins' went for the high of $20. By clue 2, the
phys ed teacher's lunch sold for twice what Mr. Armour's did. Since Mr. Armour
isn't the history teacher (9), he is making the lunch containing the peach;
and the phys ed teacher is making the roast beef sandwich. Since the phys ed
teacher isn't including the chocolate cupcake (7), by clue 10, the chocolate
cupcake is in the lunch with the peanut butter sandwich, and the science
teacher is Mr. Armour. Then Ms. Chavez teaches phys ed, and the math teacher
is making the lunch with peanut butter (6). By elimination, Mr. Eakins
teaches English. Neither Mr. Eakins (3) nor science teacher Mr. Armour (10)
is bringing the tuna salad sandwich, so the history teacher is. Mr. Armour's
sandwich choice is smoked turker and Mr. Eakins' is ham & cheese (9). By
clue 13, the vanilla pudding is in the history teacher's lunch, while the
math teacher is bringing a banana for lunch. By clue 3, Ms. Chavez likes
an orange in her lunch. Mr. Eakins' choice of dessert is M & M's, with the
grapes included in the history teacher's lunch (5). Mr. Eakins is bringing
an apple in his lunch. The grapes are in Ms. Benson's lunch and the banana
in Mr. Deberg's (5). By clue 11, Ms. Chavez is including Oreo cookies in
her lunch, and Mr. Armour is bringing a Krispy Kreme donut with his. The
five Lunch With the Teacher meals sold at auction as follows:
 $20  Mr. Eakins, English, ham & cheese, apple, M & M's
 $12  Ms. Chavez, phys ed, roast beef, orange, Oreo cookies
 $10  Ms. Benson, history, tuna salad, grapes, vanilla pudding
 $9  Mr. Deberg, math, peanut butter, banana, chocolate cupcake
 $6  Mr. Armour, science, smoked turkey, peach, Krispy Kreme donut


