baseball cards and comic books\nterry and tommy are avid collectors of baseball cards and comic books. they…

baseball cards and comic books\nterry and tommy are avid collectors of baseball cards and comic books. they went to a collectors convention recently and purchased items to add to their collections. terry purchased 5 copies of his favorite comic book and 6 packets of baseball cards. tommy purchased 8 copies of the same comic book and 4 packets of baseball cards. terry spent $54.75 and tommy spent $68.\nwrite a system of equations to model tommys and terrys purchases and then determine the cost of a comic book and the cost of a packet of baseball cards.

baseball cards and comic books\nterry and tommy are avid collectors of baseball cards and comic books. they went to a collectors convention recently and purchased items to add to their collections. terry purchased 5 copies of his favorite comic book and 6 packets of baseball cards. tommy purchased 8 copies of the same comic book and 4 packets of baseball cards. terry spent $54.75 and tommy spent $68.\nwrite a system of equations to model tommys and terrys purchases and then determine the cost of a comic book and the cost of a packet of baseball cards.

Answer

Explanation:

Step1: Define variables

Let ( x ) be the cost of a comic book and ( y ) be the cost of a packet of baseball cards.

Step2: Write equations for Terry and Tommy's purchases

For Terry: ( 5x + 6y=54.75 ) For Tommy: ( 8x + 4y = 68 )

Step3: Simplify the Tommy's equation

Divide the equation ( 8x + 4y = 68 ) by ( 4 ), we get ( 2x + y=17 ), then ( y = 17 - 2x )

Step4: Substitute ( y = 17 - 2x ) into Terry's equation

Substitute into ( 5x + 6y=54.75 ): [ \begin{align*} 5x+6(17 - 2x)&=54.75\ 5x + 102-12x&=54.75\

  • 7x&=54.75 - 102\ -7x&=-47.25\ x& = 6.75 \end{align*} ]

Step5: Find the value of ( y )

Substitute ( x = 6.75 ) into ( y = 17 - 2x ) ( y=17-2\times6.75=17 - 13.5 = 3.5 )

Answer:

The cost of a comic book is ( $6.75 ) and the cost of a packet of baseball cards is ( $3.5 )