Emily wants to buy turquoise stones on her trip to New MExico to give to at least 4 of her friends. The gift shop sells stones for either $4 or $6 per stone. Emily has no more than $30.
What are the system of inequalities so I could be able to graph them?
let the number of cheap stones be x
let the number of more expensive stones by y
4x + 6y <= 30
x + y >= 4
jaj
To represent the given problem as a system of inequalities, let's assume Emily buys x turquoise stones at $4 each and y turquoise stones at $6 each.
The first inequality represents the total number of stones Emily purchases:
x + y ≥ 4 (Emily buys stones for at least 4 friends)
The second inequality represents the total cost of the stones Emily can afford:
4x + 6y ≤ 30 (Emily has no more than $30)
Therefore, the system of inequalities is:
x + y ≥ 4
4x + 6y ≤ 30
To graph these inequalities, plot the region that satisfies both conditions. The shaded region will represent the feasible solutions.
To graph the system of inequalities for this problem, we need to define variables and set up the inequalities based on the given information.
Let's define:
x = the number of stones that cost $4 each
y = the number of stones that cost $6 each
We know that Emily wants to give at least 4 stones to her friends. Therefore, we have the inequality:
x + y ≥ 4 (since x and y can be any non-negative integers)
Additionally, we know that Emily has no more than $30 to spend. Each $4 stone and each $6 stone count towards her total spending. So, we have the inequality:
4x + 6y ≤ 30 (the total cost should not exceed $30)
Now we have the system of inequalities:
x + y ≥ 4
4x + 6y ≤ 30
To graph these inequalities, we will plot the boundary lines for each inequality (using equality instead of inequality) and then determine the feasible region. The feasible region is the area where both inequalities are satisfied.
To graph the lines, we need to rewrite each equality in the slope-intercept form (y = mx + b):
x + y = 4 --> y = -x + 4
4x + 6y = 30 --> y = (-4/6)x + 5 --> y = (-2/3)x + 5/3
Now we can graph these lines on a coordinate plane and shade the region that satisfies both inequalities.