16 factory workers made 40 pieces in a certain amount of time.
a)Do these quantities (number of workers and number of pieces produced) vary directly or inversely?
b)Find the constant of variation.

If y varies x directly, then y = kx, that means the ratio between them is constant ( [tex]\frac{y}{x}=k[/tex] ) , they increased together and decreased together, k is the constant of variation
If y varies x inversely, then yx = k, that means when x increased y must be decrease ( [tex]y=\frac{k}{x}[/tex] ) k is the constant of variation

∵ 16 factory workers made 40 pieces in a certain amount of time

- If the number of worker increased, then the number of pieces

increased in the same certain time, if the number of worker

decreased, then the number of pieces also decrease in the

same certain time

∴ The the number of workers and the number of pieces produce

vary directly

∴ Number of pieces produced = k × number of worker

a) The quantities vary directly

∵ The number of worker = 16

∵ The number of pieces produced = 40

- Substitute these values in the equation of variation above

∴ 40 = k × 16

- Divide both sides by 16

∴ k = 2.5

b) The constant of variation is 2.5

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