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Lucy earns money babysitting. Her earnings and hours worked represent a direct variation. She worked for 4 hours and earned $25.

Determine the constant of proportionality for dollars earned per hour worked

Determine the constant of proportionality for hours worked per dollar earned.

Answer :

carlosego

For this case we have that by definition, a direct variation is given in the form:

[tex]y = kx[/tex]

Where:

k: It is the constant of proportionality

According to the statement we have to:

[tex]y = 25\\x = 4[/tex]

Substituting:

[tex]25 = k4\\k = \frac {25} {4}[/tex][tex]k = 6.25\ for\ \frac {dollars} {hour}[/tex]

On the other hand we have:

[tex]y = 4\\x = 25\\4 = k25\\k = \frac {4} {25}[/tex]

[tex]k = 0.16\ for\ \frac {hours} {dollar}[/tex]

Answer:

[tex]k = 6.25 for \frac {dollars} {hour}\\k = 0.16 for \frac {hours} {dollar}[/tex]

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