A 384-m wire is cut into three pieces. The second piece is 3 m longer than the first. The third is four-fifths as long as the first. How long is each piece?
first ------> x
second ----> x+3
third -----> (4/5)x
solve x + x+3 + (4/5)x = 384
I suggest multiplying each term by 5, then it becomes real easy.
F-lenght of first size
S-lenght of second size
T-lenght of third size
S=F+3
T=(4/5)*F
F+S+T=F+F+3+(4/5)F=384
2F+3+(4/5)F=384
2F+(4/5)F=384-3
2F+(4/5)F=381 Multiply with 5
10F+4F=381*5
14F=1905 Divide with 14
F=1905/14
S=F+3=(1905/14)+(42/14)
Becouse (42/14)=3
S=1947/14
T=(4/5)*F=(4/5)*(1905/14)
=(4/5)*[(3*5*127)/14]
Becouse 1905=3*5*127
T=(4*3*127)/(14)=1524/14
T=1524/14
F+S+T=(1905/14)+(1947/14)+(1524/14)
=5376/14=384
To find the lengths of each piece, let's assign variables to represent their lengths.
Let x be the length of the first piece.
The second piece is 3 m longer than the first, so its length is x + 3.
The third piece is four-fifths as long as the first, so its length is (4/5)x.
According to the problem, the total length of the wire is 384 m. Therefore, we can write the equation:
x + (x + 3) + (4/5)x = 384
Now, let's solve the equation to find the value of x:
x + x + 3 + (4/5)x = 384
Multiplying the entire equation by 5 to eliminate the fraction:
5x + 5x + 15 + 4x = 1920
14x + 15 = 1920
Subtracting 15 from both sides of the equation:
14x = 1905
Dividing both sides of the equation by 14:
x = 135
Now that we have found x to be equal to 135, we can substitute this value back into each piece's length equation to find their lengths:
First piece: x = 135 m
Second piece: x + 3 = 135 + 3 = 138 m
Third piece: (4/5)x = (4/5) * 135 = 108 m
Therefore, the lengths of the three pieces are:
First piece: 135 m
Second piece: 138 m
Third piece: 108 m