Three families visited the local fair over a holiday weekend: the rawlins family spent $51 on admission for 2 children and 3 adults, plus 50 carnival tickets. the alvarez family spent $90 on admission for 4 children and 6 adults, plus 100 carnival tickets. the talbot family spent $78 on admission for 2 children and 5 adults, plus 80 carnival tickets. which matrix equation can be solved to find the cost of admission for children, x, the cost of admission for adults, y, and the cost of each carnival ticket, z

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13-06-2022
Mathematics

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Three families visited the local fair over a holiday weekend: the rawlins family spent $51 on admission for 2 children and 3 adults, plus 50 carnival tickets. the alvarez family spent $90 on admission for 4 children and 6 adults, plus 100 carnival tickets. the talbot family spent $78 on admission for 2 children and 5 adults, plus 80 carnival tickets. which matrix equation can be solved to find the cost of admission for children, x, the cost of admission for adults, y, and the cost of each carnival ticket, z

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AFOKE88 AFOKE88 · Answer 1 · 2022-06-24T19:37:51+02:00

The matrix equation that can be solved to find all the respective costs is;

[tex]\left[\begin{array}{ccc}2&3&50\\4&6&100\\2&5&80\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}51\\90\\78\end{array}\right][/tex]

How to create matrix equations?

Let cost of admission for children be x.

Let cost of admission for adults be y.

Let cost of admission for carnival tickets be z.

Thus, we have the simultaneous equation as;

2x + 3y + 50z = 51

4x + 6y + 100z = 90

2x + 5y + 80z = 78

Thus, writing this in matrix form gives;

[tex]\left[\begin{array}{ccc}2&3&50\\4&6&100\\2&5&80\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}51\\90\\78\end{array}\right][/tex]

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