Question

solve for z in the proportion.
\frac{7}{5} = \frac{84}{z}
z = \boxed{}

Explanation:

Step1: Cross - multiply the proportion

Given the proportion $\frac{7}{5}=\frac{84}{z}$, cross - multiplying (which is based on the property of proportions: if $\frac{a}{b}=\frac{c}{d}$, then $a\times d = b\times c$) gives us $7\times z=5\times84$.

Step2: Simplify the right - hand side

Calculate $5\times84 = 420$. So the equation becomes $7z = 420$.

Step3: Solve for z

Divide both sides of the equation $7z = 420$ by 7. That is $z=\frac{420}{7}$.

Step4: Calculate the value of z

$\frac{420}{7}=60$.

Answer:

60