Answer:
The value of x when y equals 30 is 12.
Step-by-step explanation:
Mathematical Equation:
[tex]\LARGE\text{$y=kx$}[/tex]
For the constant of variation (k):
Given: [tex]y=40[/tex], [tex]x=16[/tex]
Find: [tex]k=?[/tex]
Formula: [tex]y=kx[/tex]
Solution:
[tex]y=kx\\40=16k\\\frac{40}{16}=\frac{16k}{16}\\k=\frac{40}{16}\\k=\frac{5}{2}[/tex]
For the value of x:
Given: [tex]k=\frac{5}{2}[/tex], [tex]y=30[/tex]
Find: [tex]x=?[/tex]
Formula: [tex]y=kx[/tex]
Solution:
[tex]y=kx\\30=\frac{5}{2}x\\5x=(30)(2)\\5x=60\\\frac{5x}{5}=\frac{60}{5}\\\boxed{\boldsymbol{x=12}}[/tex]
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