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Jerome bought 15 videos from a department store. Some videos were new releases, x, which cost $19, and some videos were classics, y, which cost $8. He spent a total of $164 on the videos. Which system of equations is set up correctly to model this information? x y = 15. 19 x 8 y = 164. X y = 15. 8 x 19 y = 164. X y = 164. 19 x 8 y = 15. X y = 15. 19 x minus 8 y = 164.

Respuesta :

To solve the problem we will find the number of videos bought by Jerome and the total cost of all the videos.

The system of equations that model this information are:

  1. 15 = x + y
  2. 164 = 18x + 9y.

Explanation

Given to us

  • Total amount spent by Jerome = $164
  • Total videos bought by Jerome = 15
  • Number of classic videos bought = y
  • Number of new release videos bought = x
  • Cost of a classic video = $8
  • Cost of a new release video = $19

Total cost of all new release videos

= Number of new releases bought x Cost of a new release video

[tex]= x \times \$19\\ =19x[/tex]

Total cost of all classic videos

= Number of classic videos bought x Cost of a classic video

[tex]= y \times \$8\\ =8 y[/tex]

Total videos bought by Jerome

Total videos bought by Jerome

= Number of new releases bought + Number of classic videos bought

15 = x + y

Total amount spent by Jerome

Total amount spent by Jerome

= Total cost of all new release videos + Total cost of all classic videos

$164 = 19x + 8y

164 = 19x +8y

Hence, the system of equations that model this information are:

  1. 15 = x + y
  2. 164 = 18x + 9y.

Learn more about System of Equations:

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