She watched 5 documentary videos, 1 cartoon video, and 4 vine compilation videos
Step-by-step explanation:
The given is;
- Andrea watched 10 videos online this week
- The documentaries are 1 hour long, the cartoons are 20 minutes long, and the vine compilations are 15 minutes long
- The number of documentaries she watched was equal to the number of times she watched the other two types of videos combined
- She watched videos for a total of 6 hours and 20 minutes
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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