Problem Solving Using Linear Function

Problem:A student who wants to earn some extra money during the summer vacation has decided to work as an assistant in a nursery summer school. She will be paid ₱60 daily for a two-hour duty. If she saves all her earnings, can you determine how many days she will have to work in order to save enough money to buy blouse that costs ₱400 and a pair of shoes that is sold for ₱500?

What computations did you use to solve the problem? If you had worked out the solution correctly, then you should have determined how long it would take for her fixed savings to reach ₱900, which is the combined amount of her intended purchases. Each day, her savings increase by a constant amount of ₱60, which shows that her total savings is a linear function of the number of days that she works. The following table shows her savings against the number of days she works. Can you fill in the last entry in the second column?

Number of days Savings1 60 = 60(1)2 120 = 60(2)3 180 = 60(3)x y = ?

You probably came up with the answer by just dividing the required amount, ₱900, by ₱60 to get the correct answer of 15 days. You may not have realized that you were in fact using the linear function defined by y = 60x, where x is the number of days, and y is the amount saved after x days. See how naturally linear functions arise in real life?In solving problems involving linear functions, it is best to first find the equation defining the function and then use it to solve for the required quantities.

In each of the following problems, form the linear function that describes the relationship between the given quantities.1. the perimeter P and the measure s of each side of a square2. the circumference C and the radius r of a circle3. the total cost C of manufacturing x units of a certain product; the fixed cost is ₱5000, and the unit cost is ₱754. the total fare F that a taxi passenger must pay for riding a total distance of x km; the flagdown rate is ₱25 for the first 300 meters and ₱10 for each succeeding 200 meters.5. the volume V of liquid inside a graduated cylinder whose base radius is 4 cm when the level of the liquid is h cm

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