Math Problem Statement
Solution
The problem involves solving a system of inequalities where Mamadou is working two jobs:
- Tutoring job: $18 per hour.
- Clearing tables job: $10 per hour.
You need to find the values for the number of hours tutoring (denoted by ) and clearing tables (denoted by ) that satisfy the following conditions:
-
Mamadou can work no more than 11 total hours in the week:
This gives the inequality:
which is expressed as . -
Mamadou must earn at least $130. His earnings are $18 per hour tutoring and $10 per hour clearing tables:
This gives the inequality:
which can be rearranged to .
Next, you need to graph these inequalities and find a solution that satisfies both.
Interpretation of the Graph:
- The shaded region represents all points that satisfy both inequalities.
- The graph should intersect within this shaded area.
From the graph you uploaded, it looks like we can observe the feasible region formed by the intersection of the two inequalities. Based on this, you can pick any valid coordinate from the intersection to give one solution for hours tutoring and clearing tables.
Let me know if you'd like to proceed with further steps or if you'd like a deeper explanation of the inequalities!
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Math Problem Analysis
Mathematical Concepts
Linear Inequalities
Systems of Equations
Graphing Solutions
Formulas
x + y ≤ 11
18x + 10y ≥ 130
Theorems
Graphing Inequalities
Intersection of Solution Sets
Suitable Grade Level
Grades 8-10
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