Math Problem Statement
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:
- (a) Write the mathematical model.
- (b) Is this mathematical model a system of linear inequalities?
- (c) Draw the graph.
- (d) Determine the coordinates of the points of intersection.
Solution Steps:
-
(a) Mathematical Model: Let:
- = hours spent delivering goods.
- = hours spent washing dishes.
The following constraints apply:
- The total number of hours cannot exceed 10:
- Besar needs to earn at least Rp120,000:
Therefore, the system of inequalities is:
x + y \leq 10 \\ 15000x + 9000y \geq 120000 \\ x \geq 0, y \geq 0 \end{cases}$$ -
(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
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