Question

Write and solve an equation to find the value of the variable.

A carpenter cut four lengths of wood. The lengths were in., mc011-2.jpg in., mc011-3.jpg in., and z in. If the mean of the lengths is mc011-4.jpg in., what was the length of the fourth piece of wood the carpenter cut?



in.


in.


in.


in.

Answer 1

To find the length of the fourth piece of wood (denoted as \( z \)), we first need the lengths of the other three pieces of wood. Since you used images (like mc011-2.jpg), I cannot see those. Please provide the lengths of the first three pieces directly, or substitute their values as needed.

Assuming the three lengths of wood are \( a \), \( b \), and \( c \), we can set up the equation based on the mean of the lengths being a known value \( m \).

The formula for the mean of four lengths is:

\[
\text{Mean} = \frac{a + b + c + z}{4}
\]

If we let \( m \) be the mean, then we can solve for \( z \):

\[
m = \frac{a + b + c + z}{4}
\]

Multiplying both sides by 4 gives:

\[
4m = a + b + c + z
\]

Now, to isolate \( z \), we rearrange the equation:

\[
z = 4m - (a + b + c)
\]

Now, substitute \( a \), \( b \), \( c \), and \( m \) with the respective values to find \( z \).

If you can provide me with the lengths of the first three pieces and the mean, I can help you further in calculating \( z \).