Question

Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $10, and each wrench costs $6. If the solution region represents the number of hammers and wrenches that Brody can buy given his budget, determine which graph represents the solution set to the system of inequalities representing this situation.

Answer 1

The graph in the attached figure

Explanation:

Let

x------> the number of hammers

y------> the number of of wrenches

we know that

`10x+6y\leq 120` -----> inequality A

`x+y\geq 14` -----> inequality B

using a graphing tool

The solution of the system of inequalities is the shaded area

see the attached figure

Answer 2

For this case, the first thing we must do is define variables:
x: number of hammers
y: number of wrenches
We write the system of inequations:
10x + 6y <= 120
x + y> = 14
We graph the system of inequations.
The solution set is given by the shaded region of the graph.
Answer:
see attached image.