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Question 1164688: You have a part-time job that pays Php150 per hour. If you work more than 40 hours, you will be paid an additional 20 pesos for the succeeding hours until the 50th hour. Beyond that, you are already paid 1.5 times your hourly rate. Represent these with a function and sketch the graph of the pay per unit hour.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe you meant 40 hours rather than 400 hours.
a php is a philippine peso.
your function is as follows:
let x = the number of hours.
let y = the number of philippine pesos.
y = 150 * x for 0 <= x <= 40
y = 150 * 40 + 170 * (x - 40) for 40 < x <= 50
y = 150 * 40 + 170 * 10 + 1.5 * 150 * (x - 50) for x > 50
simplify these equations to get:
y = 150 * x for 0 <= x <= 40
y = 6000 + 170 * (x - 40) for 40 < x <= 50
y = 7700 + 225 * (x - 50) for x > 50
to use these equations, you have to know the total hours worked.
for example:
if you worked 30 hours, then your pay is 150 * 30 = 4500 pesos.
if you worked 45 hours, then your pay is 6000 + 5 * 170 = 6850 pesos.
if you worked 72 hours, then you pay is 7700 + 225 * 22 = = 12650 pesos.
to confirm this is correct, then just break it down into its constituent parts and calculate each separately.
when you worked 30 hours, the pay is 150 * 30 = 4500 pesos.
when you worked 45 hours, you got payed 40 * 150 plus 5 * 170 = 6850 pesos.
when you worked 72 hours, you got payed 40 * 150 plus 10 * 170 + 22 * 225 = 12650 pesos.
a graph of the function would look like this:
you can see that the slope of the graph changes after x = 40 and changes again after x = 50.
the formula for slope is (y2-y1) / (x2-x1)
that's the change in y divided by the corresponding change in x.
the slope from x = 0 to x = 50 is 6000 / 40 = 150.
the slope from x = 40 to x = 50 is (7700 - 6000) / 10 = 170.
the slope from x = 50 to x = 80 is (14450 - 7700) / 30 = 225.
these slopes are the same as the hourly wages within those intervals of x.
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