Respuesta :
Answer:
(a) [tex]h = \frac{2400}{w}[/tex]
(b)300 Hours
(c)150 Hours
(d)Reduced and halved.
(e) [tex]w = \frac{2400}{h}[/tex]
Step-by-step explanation:
(a) The number of hours worked is inversely proportional to the wage.
This is written as:
[tex]h \propto \frac{1}{w} \\\text{Introducing variation constant k}\\h = \frac{k}{w}\\$Since the money to be raised is constant, k = $ \$2400\\Therefore, h = \frac{2400}{w}[/tex]
(b)If the student earns $8 an hour
w=$8
[tex]\text{Number of Hours required, h} = \frac{2400}{8} =300 Hours[/tex]
(c)When the wage per hour =$16
When w=$16
[tex]\text{Number of Hours required, h} = \frac{2400}{16} =150 Hours[/tex]
The number of hours reduced and is in fact halved.
(d)
[tex]\text{When the wage per hour =w}, h = \frac{2400}{w}\\\text{When the wage per hour =2w}, h = \frac{2400}{2w}=\frac{1}{2} X \frac{2400}{w} =\frac{h}{2}[/tex]
The effect of raising the wage from $w to $2w per hour is that the number of hours required to work is reduced and exactly halved.
(e)The wage per hour is inversely proportional to the number of hours.
In fact,
[tex]\text{From h = }\frac{2400}{w}\\\text{Cross Multiplying}\\hw=2400\\\text{Dividing both sides by h}\\w = \frac{2400}{h}[/tex]
