y varies directly as x, y = 7 when x = 21. Determine x when y = 5.
Step 1
Let
y varies directly as x, it is y depends on x, in math terms
f(x)=y
y = 7 when x = 21
f(21)=7
Determine x when y = 5. f(?)=5
Step 2
there is a proportion, this must be equal, make a rule of three to find the value
so
x y
[tex]\begin{gathered} 21\leftrightarrow7 \\ x\text{ }\leftrightarrow5 \\ \text{the relation is} \\ \frac{21}{7}=\frac{x}{5} \\ \text{solve for x} \\ x=\frac{21\cdot5}{7} \\ x=\frac{105}{7} \\ x=15 \end{gathered}[/tex]so , when y=5, x=15
