Answer:
The charity collected approximately 87 videos.
Explanation:
Given:
B = Number of books
V = Number of videos
G = Number of board games
Total number of items collected = 360
Statement 1:
The number of books that the charity collected was 40 percent of the total number of books, videos, and board games that the charity collected.
Statement 2:
The number of books that the charity collected was 66 percent of the total number of videos and board games.
From Statement 1, we have B = 0.4(B + V + G).
Expanding the equation, we have B = 0.4B + 0.4V + 0.4G.
Simplifying, we get 0.6B = 0.4V + 0.4G. Equation (1)
From Statement 2, we have B = 0.66(V + G). Equation (2)
We also know that the total number of items collected is the sum of books, videos, and board games:
B + V + G = 360. Equation (3)
Now, let's solve the system of equations (1), (2), and (3) to find the values of B, V, and G.
Substituting equation (2) into equation (1), we have:
0.6B = 0.4(0.66(V + G)) + 0.4G
0.6B = 0.264V + 0.264G + 0.4G
0.6B = 0.264V + 0.664G. Equation (4)
Substituting equation (2) into equation (3), we have:
(0.66(V + G)) + V + G = 360
0.66V + 0.66G + V + G = 360
1.66V + 1.66G = 360
V + G = 216/1.66
V + G ≈ 130.12. Equation (5)
From equations (4) and (5), we can solve for V and G:
0.264V + 0.664G = 0.6B
0.264V + 0.664G = 0.6(0.66(V + G))
0.264V + 0.664G = 0.396V + 0.396G
0.264V - 0.396V = 0.396G - 0.664G
-0.132V = -0.268G
V ≈ 2.03G. Equation (6)
Substituting V = 2.03G into equation (5), we have:
2.03G + G ≈ 130.12
3.03G ≈ 130.12
G ≈ 42.95
Substituting G ≈ 42.95 into equation (6), we have:
V ≈ 2.03(42.95)
V ≈ 87.18
Therefore,
The charity collected approximately 87 videos.