Math Problem Statement

Besar memiliki dua pekerjaan paruh waktu. Untuk mengantar barang, Besar dibayar Rp15.000,00 per jam. Untuk pekerjaan mencuci piring di restoran, Besar dibayar Rp9.000,00 per jam. Dia tidak dapat bekerja lebih dari 10 jam. Besar membutuhkan uang sebesar Rp120.000,00. Berapa jam dia harus bekerja untuk masing-masing pekerjaan?

Solution

The image contains a math word problem related to part-time work. Here's a breakdown of the problem:

Problem Summary:

  • Besar has two part-time jobs.
    • For delivering goods, Besar earns Rp15,000 per hour.
    • For washing dishes at a restaurant, Besar earns Rp9,000 per hour.
  • Besar cannot work more than 10 hours in total.
  • He needs Rp120,000.

The questions asked are:

  1. (a) Write the mathematical model.
  2. (b) Is this mathematical model a system of linear inequalities?
  3. (c) Draw the graph.
  4. (d) Determine the coordinates of the points of intersection.

Solution Steps:

  1. (a) Mathematical Model: Let:

    • xx = hours spent delivering goods.
    • yy = hours spent washing dishes.

    The following constraints apply:

    • The total number of hours cannot exceed 10: x+y10x + y \leq 10
    • Besar needs to earn at least Rp120,000: 15000x+9000y12000015000x + 9000y \geq 120000

    Therefore, the system of inequalities is:

    x + y \leq 10 \\ 15000x + 9000y \geq 120000 \\ x \geq 0, y \geq 0 \end{cases}$$
  2. (b) This system is a system of

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Math Problem Analysis

Mathematical Concepts

Linear Inequalities
Systems of Equations

Formulas

x + y ≤ 10
15000x + 9000y ≥ 120000

Theorems

Linear Systems
Graphical Solution to Inequalities

Suitable Grade Level

Grades 9-10