Question

Amy is at the store to buy shorts and pants. the shirts cost $40 each and the pants cost $50 each. she plans to spend no more than $400 and buy at least 5 items. Find a possible combination of shirts and pants she can buy. How do you know this is a solution? what are two possible ways to show that this is a solution.

tysm if u help me ☺️

Answer 1

Answer: Yes that is correct Explanation:

Answer 2

(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

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