Question

A 56-inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 5 times as long as the the first piece if x represents the length of the first piece find the length of all three pieces

Answer 1

The 1st piece = 7 inches

The 2nd piece = 14 inches

The 3rd piece = 35 inches

Explanation:

We want to find the length of three pieces of a board with a total length of 56 inches. Let x be the length of the first piece, then the length of the second piece is 2x and the length of the third piece is 5x. We can write an equation that expresses the total length of the board as the sum of the lengths of the three pieces:

• x+2x+5x=56

To solve for x, we need to simplify the equation by combining like terms on the left side:

• 8x=56

Then, we need to divide both sides by 8 to isolate x:

• 8x/8 ​= 56/8​
• x=7

This means that the first piece has a length of 7 inches. To find the lengths of the other pieces, we need to substitute x = 7 into the expressions for 2x and 5x:

• 2x=2(7)=14
• 5x=5(7)=35

Therefore, the second piece has a length of 14 inches and the third piece has a length of 35 inches. We can check our answer by adding up the lengths of the pieces and verifying that they equal the total length of the board:

• 7+14+35=56

This is true, so our answer is correct.