SOLUTION: The engines on the Great Eastern Railway all have six axles and the cars (tankers and hoppers) all have four axles. If a recent train consisted of 43 units and had 178 axles, how m
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-> SOLUTION: The engines on the Great Eastern Railway all have six axles and the cars (tankers and hoppers) all have four axles. If a recent train consisted of 43 units and had 178 axles, how m
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Question 212168: The engines on the Great Eastern Railway all have six axles and the cars (tankers and hoppers) all have four axles. If a recent train consisted of 43 units and had 178 axles, how many engines and how many cars were in the train? Note: an axle is a rod that holds a pair of wheels in place.
When it came time to discuss the problem, students were first asked to simply tell the strategy they used to approach it. As a teacher, try to put yourself in the place of the students and work the problem in the manner that you anticipate the student has worked it.
You can put this solution on YOUR website! engines have 6 axles each.
cars have 4 axles each.
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train consists of 43 units and 178 axles.
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let x = number of engines and let y = number of cars (tankers and hoppers).
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you have:
x + y = 43
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that would be one equation.
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each engine has 6 axles and each car has 4 axles.
6x + 4y = 178
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you cannot solve these equations separately but you can solve them jointly.
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you have 2 equations that need to be solved simultaneously.
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the equations are:
x + y = 43
6x + 4y = 178
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you can solve these by substitution.
you solve for one of the variables in one of the equations and then you replace that variable in the other equation.
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we'll solve for y in the first equation.
we get y = 43 - x
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we'll replace y in the second equation with 43 - x
we get:
6x + 4 * (43-x) = 178
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we expand this equation to get:
6x + 4*43 - 4x = 178
this becomes:
6x + 172 - 4x = 178
we combine like terms to get:
2x + 172 = 178
we subtract 172 from both sides of equation to get:
2x = 178 - 172 = 6
we divide both sides by 2 to get:
x = 3
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the train has 3 engines and 40 cars.
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3*6 = 18
40*4 = 160
160 + 18 = 178
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x = 3 and y = 40 looks good.
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3 + 40 = 43
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