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Write a system of equations to represent each problem2. Asna works on a shipping dock at a tire manufacturing plant. She loads a pallet with 4Mudslinger tires and 6 Roadtripper tires. The tires on the pallet weigh 212 pounds. Sheloads a second pallet with 7 Mudslinger tires and 2 Roadtripper tires. The tires on thesecond pallet weigh 184 pounds. How much does each Mudslinger tire and eachRoadtripper tire weigh?

Respuesta :

let x be the weight of a Mudslinger tire and y be the weight of a Roadtripper tire.

Then ,according to first condition

[tex]4x+6y=212[/tex]

And according to second condition :-

[tex]7x+2y=184[/tex]

So the system of equations is :-

[tex]\begin{gathered} 4x+6y=212 \\ 7x+2y=184 \end{gathered}[/tex]

In order to solve the given system multiply second equation by 3 and subtract it from first equation which gives:-

[tex]\begin{gathered} -17x=-340 \\ x=20 \end{gathered}[/tex]

Onj substituting x=20 in second equation we get:-

[tex]\begin{gathered} 7\times20+2y=184 \\ 2y=184-140 \\ 2y=44 \\ y=22 \end{gathered}[/tex]

So weight of a Mudslinger tire is 20 pounds and weight of a Roadtripper tire is 22 pounds.

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