<PRE><B>Question 212168</B>
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&#39;ll solve for y in the first equation.
we get y = 43 - x
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we&#39;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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