SOLUTION: In a series of spring training games, the Yankees scored 35 runs. The Dodgers and Tigers, respectivly, tallied half and a third as many as the Reds. The Reds' scores were as much b

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: In a series of spring training games, the Yankees scored 35 runs. The Dodgers and Tigers, respectivly, tallied half and a third as many as the Reds. The Reds' scores were as much b      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 296: In a series of spring training games, the Yankees scored 35 runs. The Dodgers and Tigers, respectivly, tallied half and a third as many as the Reds. The Reds' scores were as much below the Yankees' as the Dodgers' were the Tigers'. How many runs did each team score
Answer by arden42(16) About Me  (Show Source):
You can put this solution on YOUR website!
First, we'll put down what we already know:
Y+=+35
D+=+R%2F2
T+=+R%2F3
Y+-+R+=+T+-+D
Since we know Y already, and we can express both D and T in terms of R, lets rewrite the final equation above as:
35+-+R+=+R%2F3+-+R%2F2
Now we have an equation completely in terms of R, so we can work out R. Multiplying by 6 to eliminate fractions (makes it nicer to work with) gives us:
210+-+6R+=+2R+-+3R
Rearranging to get all the R's on one side makes it:
210+=+5R
Divide by 5:
R+=+42
Since D = R/2, and R = 42:
D+=+21
Since T = R/3, and R = 42:
T+=+14
So the final results are:
The Reds scored 42, the Yankees scored 35, the Dodgers scored 21 and the Tigers scored 14.