Answer: The lenght of the longest piece is 27 ft.
Explanation:
Hi, to solve this problem we have to write 3 equations, and combine them to calculate the value of the variables.
The pipe is 47 ft long and is going to be cut into three pieces (a,b, and c).
So:
1) a + b + c = 47
Then, the second piece is three times as long as the first piece.
2) b =3a
And finally, the third piece is two feet more than five times the length of the first piece.
3) c = 5a + 2
Now that we have the three equations, we combine equations 2) and 3) with 1).
1) a + 3a + 5a +2 = 47
Solving:
4a + 5a = 47 -2
9a =45
a = 45/9
a = 5 ft
With the value of "a", we can calculate the value of "b" and "c".
2) b= 3a
b = 3 x 5 = 15 ft
3) c = 5a + 2
c= 5x5 +2
c = 25 +2
c = 27 ft
In conclusion, the lenght of the longest piece is 27 ft.
a = 5ft ; b= 15 ft ; c= 27ft
Feel free to ask for more if it´s necessary or if you did not understand something.