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Los boletos de entrada a un juego de baloncesto para 2 adultos y 3 niños cuestan $67 y para 3 adultos y 2 niños $78. ¿Cuál es el precio del boleto del adulto?

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Lhannearaujoidn

The price of the adult ticket to a basketball game is $20.

System of Linear Equations

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

  • STEP 1 - Convert the text of problem in system of equations

                     2a+3n=67

                    3a+2n=78

where: a= adultos and n =niños

  • STEP 2 - Find the variables a and n.

                                 [tex]\begin{bmatrix}2a+3n=67\;\; equation1\\\ 3a+2n=78\;\; equation2\end{bmatrix}\\ \\ \\ \begin{bmatrix}2a+3n=67\; *(-3)\\ 3a+2n=78\; *(2)\end{bmatrix}\\ \\ \\ \begin{bmatrix}-6a-9n=-201\\ 6a+4n=156\end{bmatrix}\\ \\ \\ Sum\; of\; equations\\ \\ -6a-9n+6a+4n=-201+156\\ -9n+4n=-201+156\\ -5n=-45\\ n=\frac{-45}{-5} =9\\\\\\ Replacing\; n\; in\; equation 1\\\\2a+3*9=67\\ 2a+27=67\\ 2a=67-27\\ 2a=40\\ a=20[/tex]

Thus, a=20 and n=9.

Learn more about the system of equations here:

https://brainly.com/question/384631

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