Question

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.

Answer 1

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

Answer 2

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

Explanation:

Let the cost of DVD be x

Let the cost of games be y

So, According to question,

`2x+3y=\$15.50\\\\and\\\\3x+1y=\$12.05`

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

`2x=15.50-3y\\\\x=(15.5-3y)/(2)`

Put this value of x in second equation:

`3x+y=12.05\\\\3* (15.5-3y)/(2)+y=12.05\\\\46.5-9y+2y=12.05* 2\\\\46.5-7y=24.1\\\\46.5-24.1=7y\\\\22.4=7y\\\\(22.4)/(7)=y\\\\3.2=y`

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

`x=(15.5-3y)/(2)\\\\x=(15.5-3*3.2)/(2)\\\\x=(15.5-9.6)/(2)\\\\x=(5.9)/(2)\\\\x=2.95`

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