SOLUTION: If a piece of wood is 5cm longer than a second piece and 3 divide by 4 of the second piece is equal to 3 divide 5 of the first.What is length of second piece

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Question 720992: If a piece of wood is 5cm longer than a second piece and 3 divide by 4 of the second piece is equal to 3 divide 5 of the first.What is length of second piece
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Always define a variable for the unknowns.
Let x = the length of the first piece of wood
Let y = the second piece of wood
Now you need TWO equations to find two unknowns.
The first part of the problem statement gives us
(1) x = y + 5.
The second part gives us
(2) (3/4)*y = (3/5)*x
Solve these two equations for (x,y). You can use any of the known methods, I'll use substitution for you.
Substitute the expression for x given by (1) into (2) and get
(3) (3/4)*y = (3/5)*(y + 5) or
(4) (3/4)*y = (3/5)*y + (3/5)*5 or
(5) [(3/4) - (3/5)]*y = 3 or
(6) [(15 - 12)/20]*y = 3 or
(7) (3/20)*y = 3 or
(8) y = 20
Now put y of (8) into (1) and get
(9) x = 20 + 5 or
(10) x = 25
Let's check these two values using (2).
Is ((3/4)*20 = (3/5)*25)?
Is (15 = 15)? Yes
Answer: The first piece of wood is 25cm and the second piece is 20cm.