Question

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?

Answer 1

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

Then ,according to first condition

`4x+6y=212`

And according to second condition :-

`7x+2y=184`

So the system of equations is :-

`\begin{gathered} 4x+6y=212 \\ 7x+2y=184 \end{gathered}`

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

`\begin{gathered} -17x=-340 \\ x=20 \end{gathered}`

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

`\begin{gathered} 7*20+2y=184 \\ 2y=184-140 \\ 2y=44 \\ y=22 \end{gathered}`

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