at Redbox mike rents 2 DVD's and 3 games for total of $15.50. At the same time John rents 3 DVD's and 1 game for a total of $12.05. write a system of equations that represents this scenario. Clearly indicate what your variables represent in the context of this problem.

D = DVDs G = Games Mike's formula 2D + 3G = 15.50 John's formula 3D + 1G = 12.05 If you multiple John by three and subtract from John you get the following. -7D = -20.55 This is the same as 7D = 20.55 D = 2.94 Plugging that into John's, you get 3(2.94) + 1G = 12.05 8.82 + G = 12.05 G = 3.23

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RenatoMattice RenatoMattice · Answer 2 · 2018-11-29T07:59:25+01:00

Answer: Cost of DVD is $2.95 and cost of games is $3.2.

Step-by-step explanation:

Let the cost of DVD be x

Let the cost of games be y

So, According to question,

[tex]2x+3y=\$15.50\\\\and\\\\3x+1y=\$12.05[/tex]

Now, we will apply " Substitution Method " i.e.,

[tex]2x=15.50-3y\\\\x=\frac{15.5-3y}{2}[/tex]

Put this value of x in second equation:

[tex]3x+y=12.05\\\\3\times \frac{15.5-3y}{2}+y=12.05\\\\46.5-9y+2y=12.05\times 2\\\\46.5-7y=24.1\\\\46.5-24.1=7y\\\\22.4=7y\\\\\frac{22.4}{7}=y\\\\3.2=y[/tex]

Now, substitute the value of y in equation of x:

[tex]x=\frac{15.5-3y}{2}\\\\x=\frac{15.5-3\times3.2}{2}\\\\x=\frac{15.5-9.6}{2}\\\\x=\frac{5.9}{2}\\\\x=2.95[/tex]

Hence, Cost of DVD is $2.95 and cost of games is $3.2.