Need help with a word problem!

[ELeathers]

Hey guys, I've been trying to solve this word problem for over an hour now. I cannot use Guess and Test on this so it has to include using a variable or making a list or something. Anyways, here's the problem and if you could help that would be wonderful. Thanks!

Sam and Josh both collect miniature ninja figures. Originally, Sam had three times as many ninjas as Josh. Then Sam traded five of his red ninjas for three of Josh's blue ninjas. Next, Josh traded four red ninjas for 7 of Sam's black ninjas. After these trades, Sam had 14 more ninjas than Josh. How many ninjas did Sam and Josh each originally have?

 

[tkhunny]

Hey guys, I've been trying to solve this word problem for over an hour now. I cannot use Guess and Test on this so it has to include using a variable or making a list or something. Anyways, here's the problem and if you could help that would be wonderful. Thanks!

Sam and Josh both collect miniature ninja figures. Originally, Sam had three times as many ninjas as Josh. Then Sam traded five of his red ninjas for three of Josh's blue ninjas. Next, Josh traded four red ninjas for 7 of Sam's black ninjas. After these trades, Sam had 14 more ninjas than Josh. How many ninjas did Sam and Josh each originally have?

Where's your work? For an hour's work, you shoudl have something.

Rule #1 - Name Stuff.

S = Original Number of Sam's Ninjas
J = Original Number of Josh's Ninjas

"Originally, Sam had three times as many ninjas as Josh"

Sam: S
Josh: J
S = 3*J

"Then Sam traded five of his red ninjas for three of Josh's blue ninjas"

Sam: S-5+3 = S-2
Josh: J-3+5 = J+2

"Next, Josh traded four red ninjas for 7 of Sam's black ninjas."

Sam: (S-2) - 7 + 4 = (S-2) - 3 = S-5
Josh: (J+2) - 4 + 7 = (J+2) + 3 = J+5

Ph, you're not going to make me do ALL the work, are you?