Question

Kaylee and her children went into a grocery store where they sell peaches for $1.25 each and mangos for $0.75 each. Kaylee has $15 to spend and must buy no less than 13 peaches and mangos altogether. Also, she must buy a minimum of 5 peaches. If x represents the number of peaches purchased and y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

To solve this problem, set up a system of inequalities using the given information. Graphically represent the inequalities and find the intersection of feasible regions. One possible solution is x = 5 and y = 8.

Step-by-step explanation:

To solve this problem, we need to set up a system of inequalities to represent the given information. Let x represent the number of peaches purchased and y represent the number of mangos purchased.

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• We know that each peach costs $1.25, so the cost of x peaches would be 1.25x.
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• We also know that each mango costs $0.75, so the cost of y mangos would be 0.75y.
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• The total cost, C, of the peaches and mangos must be less than or equal to $15: C ≤ 15.
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• The total number of peaches and mangos purchased, N, must be greater than or equal to 13: N ≥ 13.
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• The number of peaches purchased must be greater than or equal to 5: x ≥ 5.

Graphically, we can plot these inequalities on a coordinate plane and shade the feasible region. The intersection of all shaded regions represents the possible solution(s).

One possible solution is x = 5 and y = 8. This satisfies all the given conditions and falls within the feasible region.