A 75-inch board is cut into 2 pieces. One piece is 4 times the length of the other. Find the lengths of the 2 pieces.

The short piece is ___ inches long.

Length of the long piece = 4 times the length of the short piece Length of the short piece = 1 times the length of the short piece. Total length of both pieces = (4 + 1) = 5 times the length of the short piece.
5 times the length of the short piece = 75 inches
The length of the short piece =75 / 5 = 15 inches
Length of the long piece = 4 times the length of the short piece = 60 inches
Check: 15 + 60 = 75 inches yay

Answered by AL2006 | 2024-06-10

The shorter piece is 15 inches, and the longer piece is 60 inches. This would be a system of equations problem. If x is the shorter piece and y is the longer piece, then your two equations would be: x + y = 75 y = 4x Since the second equation tells you what y is, you can substitute the y in the first equation with 4x to get the equation x + 4x = 75. x + 4x is 5x, so you'll have 5x = 75. To get x by itself, divide off the 5 on both sides. 75 ÷ 5 = 15, so x = 15. The shorter piece would be 15 inches long. Now that you know x, go to the second equation and plug it in: y = 4·15. 4·15 is 60, so that makes the longer piece 60 inches long. Sorry if this was confusing; I'm really bad at giving written directions :/

Answered by tommoholic13 | 2024-06-10

The short piece is 15 inches long, while the long piece is 60 inches long. This is calculated by setting the short piece as x inches and the long piece as 4 x inches, leading to the equation 5 x = 75 . Solving gives x = 15 .
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Answered by AL2006 | 2024-10-16