Suppose Phil and Kate decide to drive the sports car to Nashville without stopping and they want to arrive by 5:00pm. What time
1 answer:
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Answer:
(a) Amy can buy 5 shirts and 4
(b) The combination is correct because it satisfies both inequalities
(c) The two possible ways to show that she can buy is 5 shirt and 4 pants are;
(1) Mathematically
(2) Graphically
Step-by-step explanation:
The given parameters are
The cost of each shirt = $40
The cost of each pant = $50
The amount Amy plans to spend ≤ $400
Let x represent the number of shirts Amy buys and let y represent the number of pants she buys, therefore, we have;
40 × x + 50 × y ≤ 400...(1)
x + y ≥ 5...(2)
Making y the subject of both inequalities gives;
For the inequality (1), we have;
40 × x + 50 × y ≤ 400
y ≤ (400/50) - (40/50) × x = 8 - (4/5)·x
y ≤ 8 - (4/5)·x
For the inequality (2), we have;
x + y ≥ 5
y ≥ 5 - x
Plotting both inequalities using the chart function in Microsoft Excel gives;
(a) As seen from the graph of the system of inequalities, Amy can buy 5 shirts and 4
(b) The combination of 5 shirts and 4 pants as a solution is correct because the value of the total number of the combination is larger than 5 (5 + 4 = 9 > 5) and the cost of 5 shirts plus 4 pants = $400
(c) The two possible ways to show that the combination of shirts and pants that Amy can buy is 5 shirt and 4 pants is a possible solution are;
(1) Mathematically, x = 5, y = 4
Therefore, y ≤ 8 - (4/5) × x gives;
4 ≤ 8 - (4/5) × 5 which is correct and
From y ≥ 5 - x gives;
4 ≥ 5 - 5 = 0, Which is also correct
(2) By plotting a graph of the system of inequalities as included
