Three couples in the senior class solved the mystery of the Senior Bulletin Board and received the $5400 reward. The money was divided unequally among the six students. The girls together received $2400. Sue had $200 more than Jan, and Lynn had $200 more than Sue. Tom got half as much as his girlfriend; Bob got the same amount as his girlfriend; and Matt got twice as much as his girlfriend. Who is going with whom?
Let’s use initials to represent the amount of money each person received.
We know J + S + L = J + (J + 200) + (J + 400) = 2400, so 3J + 600 = 2400 and
J = 600, S = 800, and L = 1000.
Then T + B + M = 5400 – 2400 = 3000. We have 6 possibilities to check:
L + .5J + 2S = 2900
L + 2J + .5S = 2600
S + .5L + 2J = 2500
S + 2L + .5J = 3100
J + .5L + 2S = 2700
J + 2L + .5S = 3000 — bingo!
So Bob is going with Jan, Matt is going with Lynn, and Tom is going with Sue.