Math Problem Statement

Write the function for each problem: 1. Adam found an offer of PLN 9 for computer activation. The shop earns an additional PLN 8 per device. Write the formula. 2. Ananda's family has a fixed monthly charge of PLN 1080 for car maintenance. Express the total cost as a function of family members using the car. 3. A computer shop charges 75 zł per hour for the first two hours, with an additional 10 zł per hour after that. Express the rental fee using a function.

Solution

The image contains four math problems asking for expressions or functions to represent given scenarios.

Problem III

  1. Adam managed to find an offer of PLN 9 for the activation of a computer. Shop earns additional PLN 8 on each activated device.

    • Write a formula to represent the total profit P(x)P(x) the shop earns after activating xx devices.
  2. Ananda family had PLN 1080 of fixed charges for maintenance of their family car a month.

    • Express the total cost CC as a function of xx number of family members using the car.

Problem IV

  1. Write the price-time function for the given problem:
    • A computer shop charges 75 zł per hour for the first two hours and an additional 10 zł per hour for each subsequent hour. Express the total computer rental fee using the function T(x)T(x), where xx is the number of hours you spend on the computer.

Solutions:

  1. For Adam's profit formula: P(x)=9x+8x=17xP(x) = 9x + 8x = 17x Here, 9 PLN for each device + 8 PLN additional profit per device.

  2. For Ananda family's maintenance cost formula: C(x)=1080+(numberofothermonthlyfactorsadded)C(x) = 1080 + (number of other monthly factors added)

    If factors are static, this becomes linear at ( C(x) = y + any_other_measurable_factor_in_zlotys+additional_hourly_ways_formulaT(x) means charges_total/rentals).]

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Piecewise Functions

Formulas

P(x) = 9x + 8x
C(x) = 1080 + additional members' costs
T(x) = 75(2) + 10(x - 2) for x > 2

Theorems

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Suitable Grade Level

Grades 7-9