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Ramblin Roy is a dirt bike boy. One day he drives his dirt bike over to a big race. There were 178 vehicles at the race, a mix of cars and dirt bikes. Altogether there were 602 wheels on the vechicles. How many cars were there ( x) ? How many dirt bikes were there ( y ) ? A. ( 55, 123 ) B. ( 123, 55 ) C. ( 178 , 602 ) D. None of the above

Respuesta :

There are x cars and y bikes.

The equation for the total number of vechiles is,

[tex]\begin{gathered} x+y=178 \\ y=178-x \end{gathered}[/tex]

In a car, there are 4 vechiles and in a bike there are two wheels. So the equation for the wheels,

[tex]\begin{gathered} 4x+2y=602 \\ 2x+y=301 \end{gathered}[/tex]

Substitute (178 - x) for y in the equation 2x + y = 301 to obtain the value of x.

[tex]\begin{gathered} 2x+178-x=301 \\ x=301-178 \\ =123 \end{gathered}[/tex]

Substitute 123 for x in the equation y = 178 - x to obtain the value of y.

[tex]\begin{gathered} y=178-123 \\ =55 \end{gathered}[/tex]

So number of cars are 123 and number of bikes are 55. So correct option is

B. ( 123, 55 )

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