She watched 5 documentary videos, 1 cartoon video, and 4 vine compilation videos
Step-by-step explanation:
The given is;
We need to find how many of each type of video she watched
Assume that the number of documentaries video is x, the number of cartoons video is y and the number of the vine compilations is z
∵ Andrea watched 10 videos
∵ x represents the number of documentary videos
∵ y represents the number of cartoon videos
∵ z represents the number of the vine compilation videos
∴ x + y + z = 10 ⇒ (1)
∵ The documentaries are 1 hour long
- Change it to minutes
∵ 1 hour = 60 minutes
∴ The documentaries are 60 minutes long
∵ The cartoons are 20 minutes long
∵ The vine compilations are 15 minutes long
∵ She watched videos for a total of 6 hours and 20 minutes
- Change it to minutes
∴ She watched videos for a total = 6 × 60 + 20 = 360 + 20 = 380
∴ She watched videos for a total 380 minutes
∴ 60x + 20y + 15z = 380 ⇒ (2)
∵ The number of documentaries she watched was equal to the number
  of times she watched the other two types of videos combined
∴ x = y + z ⇒ (3)
Substitute equation no (3) in equations (1) and (2)
- Substitute x in equation (1) by (y + z)
∵ (y + z) + y + z = 10
- Add like terms
∴ 2y + 2z = 10
- Divide all terms by 2 to simplify the equation
∴ y + z = 5 ⇒ (4)
- Substitute x by (y + z) in equation (2)
∵ 60(y + z) + 20y + 15z = 380
∴ 60y + 60z + 20y + 15z = 380
- Add like terms
∴ 80y + 75z = 380
- Divide all terms by 2 to simplify the equation
∴ 16y + 15z = 76 ⇒ (5)
Solve equations (4) and (5) to find y and z
Multiply equation (4) by -15 to eliminate z
∵ -15y - 15z = -75 ⇒ (6)
- Add equations (5) and (6)
∴ y = 1
Substitute y in equation (4) by 1 to find z
∵ 1 + z = 5
- Subtract 1 from both sides
∴ z = 4
Substitute y by 1 and z by 4 in equation (3)
∵ x = 1 + 4
∴ x = 5
She watched 5 documentary videos, 1 cartoon video, and 4 vine compilation videos
Learn more:
You can learn more about solving the system of equations in brainly.com/question/2115716
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