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A sporting goods salesperson sells 2 fishing reels and 5 rods for $365. Thenext day, the sales person sells 4 reels und 2 rods for S290. How much does each cost?(Solve by Setting-up a system of two equations in two variables)

Respuesta :

Let's use the variable x to represent the cost of one fishing reel and the variable y to represent the cost of one rod.

If 2 fishing reels and 5 rods cost $365, we have the equation:

[tex]2x+5y=365[/tex]

Then, if 4 reels and 2 rods cost $290, we have the second equation:

[tex]4x+2y=290[/tex]

Let's divide the second equation by 2 and isolate the variable y:

[tex]\begin{gathered} 2x+y=145 \\ y=145-2x \end{gathered}[/tex]

Then, let's use this value of y in the first equation:

[tex]\begin{gathered} 2x+5(145-2x)=365 \\ 2x+725-10x=365 \\ -8x=365-725 \\ -8x=-360 \\ x=45 \\ \\ y=145-2\cdot45 \\ y=145-90 \\ y=55 \end{gathered}[/tex]

So the cost of one reel is $45 and the cost of one rod is $55.

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