Question

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 1

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

`y = kx`

Where:

k: It is the constant of proportionality

According to the statement we have to:

`y = 25\\x = 4`

Substituting:

`25 = k4\\k = \frac {25} {4}`
`k = 6.25\ for\ \frac {dollars} {hour}`

On the other hand we have:

`y = 4\\x = 25\\4 = k25\\k = \frac {4} {25}`

`k = 0.16\ for\ \frac {hours} {dollar}`

Answer:

`k = 6.25 for \frac {dollars} {hour}\\k = 0.16 for \frac {hours} {dollar}`