Question 49185: Hello,
My daughter has not received her book yet. This is 7th grade prealgebra. A word problem was written on the board as follows:
3 ducks and 2 ducklings weight 32 ounces, 4 ducks and 3 ducklins weigh 44 ounces. All the ducks weigh the same and all ducklings weigh the same. What would 2 ducks and 1 duckling weigh? He gave the following answer which we can not understand: (3D+2d=32)3=9D+6d=96; (4D+3d=44)-2=(-8D+-6d)=-88; 3(8)+2d=32, 24+2d=32, 24+2d-24=32-24, 2d=8, 2d*8=16d, 16d, d =4+16=20. Please help
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Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let D = the weight of 1 Duck.
Let d = the weight of 1 duckling.
From the problem description, you can write a system of equations.
1) 3D + 2d = 32 (3 Ducks (D) and (+) 2 ducklings (d) weigh 32 ounces.)
2) 4D + 3d = 44 (4 Ducks (D) and (+) 3 ducklings (d) weigh 44 ounces.)
To solve this system of equations, multiply equation 1) by 3 and equation 2) by -2, then add the two equations.
1a) 3(3D + 2d = 32) -> 1b) 9D + 6d = 96
2a) -2(4D + 3d = 44) -> 2b) -8D - 6d = -88 Add these two equations, 1b)+2b).
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........................D = 8 One Duck weighs 8 ounces. Now substitute this into equation 1) and solve for d.
1) 3(8) + 2d = 32
24 + 2d = 32 Subtract 24 from both sides of the equation.
2d = 8 Divide both sides by 2.
d = 4 One duckling weighs 4 ounces.
Finally, 2 Ducks and 1 duckling = 2D + 1d = 2(8) + 1(4) = 16 + 4 = 20 ounces.
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