SOLUTION: Please help me figure out how to solve this problem. Together a baseball and a football weigh 1.25 pounds, the baseball and soccer ball weigh 1.35 pounds, and the football and t

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Question 257654: Please help me figure out how to solve this problem.
Together a baseball and a football weigh 1.25 pounds, the baseball and soccer ball weigh 1.35 pounds, and the football and the soccer ball weigh 1.6 pounds. How much does each of the balls weigh?
Thank you!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start by assigning variables to the unknown quantities:
B = weght of baseball.
S = weight of soccer ball.
F = weight of football.
From the problem description:
1) B+F = 1.25 lbs.
2) B+S = 1.35 lbs.
3) F+S = 1.6 lbs.
Now you have a system of three equations with three unknowns and this is solvable.
Rewrite equation 1) as (B = 1.25-F) and substitute into equation 2) to get:
2a) (1.25-F)+S = 1.35
Now rewrite equation 3) as (S = 1.6-F) and substitute into equation 2a) to get:
2b) (1.25-F)+(1.6-F) = 1.35 Simplify and solve for F.
2c) 2.85-2F = 1.35 Add 2F to both sides.
2d) 2.85 = 1.35+2F Now subtract 1.35 from both sides.
2e) 1.5 = 2F Finally, divide both sides by 2.
highlight%280.75+=+F%29 The football weighs 0.75 lbs.
Now that you know the weight of the football (F = 0.75) you can substitute this into equations 1) and 3) to solve for B and S respectively.
I'll leave this for you to finish up.
Good luck!