Final answer:
To find the total length of the three pieces, we need to set up a system of equations. However, the given information does not provide enough information to solve the system and determine the lengths of the pieces or their total length.
Step-by-step explanation:
To find the total length of the three pieces, we need to add their lengths together. From the given information, it is stated that two of the pieces add together to give the resultant length of 10 units, and all three pieces add together to give the resultant length of 15 units. Therefore, we can set up the equation: x + y = 10 and x + y + z = 15, where x, y, and z are the lengths of the three pieces. We can solve this system of equations to find the values of x, y, and z, and then find the total length by adding them together.
From the first equation, we can solve for x in terms of y: x = 10 - y. Substituting this value of x into the second equation, we get (10 - y) + y + z = 15. Simplifying this equation, we get 10 + z = 15, which implies that z = 5. Substituting this value of z back into the first equation, we get x + y = 10, or x + y = 10 - 5 = 5. From this equation, we can solve for y in terms of x: y = 5 - x.
Now, substituting the value of y into the equation x + y + z = 15, we get x + (5 - x) + 5 = 15. Simplifying this equation, we get 10 = 15, which is not true. This means that there is no solution to the system of equations, and we cannot determine the lengths of the three pieces or their total length with the given information.