John is at a local bait shop; he wants to buy bait for his fishing trip. At the store, they are selling live bait for $12 a pound and natural bait for $7 a pound. John would like to get at least 3 pounds of live bait, but he only has a budget of $63. Let
x
be the amount of live bait and
y
be the amount of natural bait.
Model the scenario with a system of inequalities.
Graph the system of inequalities and use complete sentences to explain which part of your graph will satisfy the two equations.
no one has the answer i need it ASAP!!!!
hey! i am not great w graphs BUT the system of inequalities are x ≥ 3 and 12x + 7y ≤ 63
hope this kinda helps!
To model the scenario with a system of inequalities, we can set up the following equations:
1. John wants to get at least 3 pounds of live bait:
x ≥ 3
2. John has a budget of $63:
12x + 7y ≤ 63
To graph the system of inequalities, we can first graph the equation x ≥ 3 as a solid line. This line represents the boundary where John gets exactly 3 pounds or more of live bait.
Next, we can graph the equation 12x + 7y ≤ 63 as a shaded region below the line. This shaded region represents all the possible combinations of pounds of live bait (x) and natural bait (y) that John can buy within his budget.
The part of the graph that satisfies both inequalities is the overlapping region between the solid line and the shaded region. This region represents the possible solutions that satisfy John's requirement of getting at least 3 pounds of live bait and staying within his budget of $63.
To model the scenario with a system of inequalities, let's consider the constraints and variables:
Constraints:
1. John wants at least 3 pounds of live bait (x >= 3).
2. John's budget is $63, so the total cost of bait must be within this limit (12x + 7y <= 63).
Variables:
Let x represent the amount of live bait (in pounds).
Let y represent the amount of natural bait (in pounds).
Based on the constraints and variables, we can form the system of inequalities as follows:
x >= 3 (Constraint 1 - John wants at least 3 pounds of live bait)
12x + 7y <= 63 (Constraint 2 - The total cost of bait must be within John's budget)
To graph this system of inequalities, plot the solution region for each inequality on a coordinate plane:
1. Graph the line x = 3, which is a vertical line passing through x = 3.
2. Graph the line 12x + 7y = 63. Rewrite it in slope-intercept form: y = (-12/7)x + 9. Plot this line by finding two points on the line and connecting them with a line.
The solution region where the two lines intersect represents the values of x and y that satisfy both inequalities. In this case, it represents the possible combinations of live bait and natural bait that meet John's requirements (at least 3 pounds of live bait and within his budget).
To identify which part of the graph satisfies both inequalities, examine the region where the shaded areas for the two inequalities overlap. This intersection represents the feasible region that satisfies both constraints. Any point within this region corresponds to a valid solution for John's bait purchase.
Please note that without a visual representation, it's challenging to provide a precise description of the exact coordinates or shape of the graph. It is recommended to consult a graphing calculator or software to visualize the system of inequalities accurately.