math problem?
A piece of wood is cut into three pieces in the ratio 2:3:5. If the longest piece is 15 in longer than the shortest piece, find the lengths of the piece of wood.
The lengths of the piece of wood in ascending order are __in, __in and __in.
Comments
If the ratios are 2:3:5, then their lengths can be represented as:
2x, 3x, and 5x.
If the longest piece is 15 in longer than the shortest, then you have this equation:
5x = 2x + 15
Now you have an equation that can be solved. Subtract 2x from both sides:
3x = 15
and divide:
x = 5
So now we know the multiplier.
Since the lengths are:
2x, 3x, and 5x
Substitute 5 in for x, and we get:
10, 15, and 25 in pieces.
Ratio = 2:3:5
Therefore, length of each piece = 2x, 3x, 5x
Given, 5x = 2x + 15
3x = 15
x = 5
Therefore, length of each piece = 10, 15, 25 inches
The lengths are 2*x, 3*x and 5*x.
5*x - 2*x = 15
3*x = 15
x = 5
Hence the lengths are 10, 15 and 25 inches.
Let longest piece be x m
Shortest piece = x - 15 cm
Piece 1_____Piece 2____Piece 3
x - 15_________________x
2____________3_______ 5
[ x - 15 ] / 2 = x / 5
5x - 75 = 2x
3x = 75
x = 25
Piece 1_____Piece 2____Piece 3
10 ins_______15 ins_____25 ins