Question

A contractor has at most $42 to spend on nails for a project. Finishing nails cost $0.45 per pound and common nails cost $0.60 per pound. He would like to purchase at least at least 30 pounds of nails total.

Answer 1

Question:

A contractor has at most $42 to spend on nails for a project. Finishing nails cost $0.45 per pound and  common nails cost $0.60 per pound. He would like to purchase at least 30 pounds of nails total. Write a system of linear inequalities

Answer:

The system of linear inequalities are:

$x + y\geq 30\\\\0.45x+0.60y\leq 42$

Solution:

Let "x" be the pounds of finishing nails

Let "y" be the pounds of common nails

Given that,

He would like to purchase at least 30 pounds of nails total.

"at least" means that he can purchase 30 pounds or more than 30 pounds also

So, we have to use "greater than or equal to" symbol

$x + y\geq 30$

From given,

Cost of 1 pound of finishing nail = $ 0.45

Cost of 1 pound of common nail = $ 0.60

A contractor has at most $42 to spend on nails for a project

"at most" means he can spend 42 or less than 42

So we have to use " less than or equal to" symbol

Thus we frame a inequality as:

$x \times 0.45 + y \times 0.60\leq 42\\\\0.45x + 0.60y\leq 42$

Thus the system of inequalities are:

$x + y\geq 30\\\\0.45x+0.60y\leq 42$