Let's solve the given equation step by step:
1) The given equation is:
[tex]\[
\frac{z}{40} = \frac{16}{32}
\][/tex]
2) To solve for \( z \), we can use the method of cross-multiplication. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction.
3) By cross-multiplying, we get:
[tex]\[
z \times 32 = 40 \times 16
\][/tex]
4) Now, calculate the right-hand side:
[tex]\[
40 \times 16 = 640
\][/tex]
So, the equation simplifies to:
[tex]\[
32z = 640
\][/tex]
5) To isolate \( z \), divide both sides of the equation by 32:
[tex]\[
z = \frac{640}{32}
\][/tex]
6) Finally, calculate the division:
[tex]\[
\frac{640}{32} = 20
\][/tex]
Therefore, the value of \( z \) is:
[tex]\[
z = 20
\][/tex]
