The length of all three pieces are 6 inches, 12 inches, and 30 inches
Step-by-step explanation:
The given is:
1. A 48 inch board is to be cut into 3 pieces
2. The second piece is twice as long as the first piece
3. The third piece is 5 times as long as the first piece
4. x represents the length of the first piece
We need to find the length of all three pieces
∵ The length of the 1st piece is x inches
∵ The length of the 2nd piece is twice as long as the 1st piece
∴ The length of the 2nd piece = 2 x inches
∵ The length of the 3rd piece is 5 times as long as the 1st piece
∴ The length of the 3rd piece = 5 x inches
∵ The length of the board is 48 inches
- Add the lengths of the three pieces and equate the sum by 48
∴ x + 2 x + 5 x = 48
∴ 8 x = 48
- Divide both sides by 8
∴ x = 6
∵ The lengths of the three pieces are x , 2 x , 5 x
∵ x = 6 inches
∴ 2 x = 2(6) = 12 inches
∴ 5 x - 5(6) = 30 inches
The length of all three pieces are 6 inches, 12 inches, and 30 inches
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