Question

getting ready for soccer season, a coach purchased 6 practice cones and a portable goal for$23. On another trip to the sporting goods store, the coach purchased 4 more cones and 2 more goals, spending $42. find the cost of a practice cone and a portable goal

Answer 1

`Let\: x,y \: (x,y>0) \: be \: the \: price \: of \: a \: cone \: and \: a \: goal \: consecutively. \\We \: have \: a \: system \: of \: equation: \\ \begin{cases}6x + y = 23 \\4x + 2y = 42 \end{cases} \\ \Leftrightarrow \begin{cases} 12x + 2y = 46\\4x + 2y = 42 \end{cases} \\ \Leftrightarrow \begin{cases}8x = 4 \\ y = 21 - 2x\end{cases} \\ \Leftrightarrow \begin{cases} x = (1)/(2) \\y = 20 \end{cases} \\ A \: practice \: cone \: cost \: 50 \: cents, a \: goal \: cost \: \$ 20`

Answer 2

He will have $22 because 6 Plus 17= 22