Marques and his children went into a grocery store and will buy peaches and mangos. Each peach costs $1.50, and each mango costs $2. Write an inequality that would represent the possible values for the number of peaches purchased (P) and the number of mangos purchased (M).

A. [tex]1.5P + 2M \leq 20[/tex]
B. [tex]2P + 1.5M \leq 20[/tex]
C. [tex]1.5P + 2M \geq 20[/tex]
D. [tex]2P + 1.5M \geq 20[/tex]

The budget constraint for Marques' purchase of peaches and mangos, with the provided costs and a total budget of $20, is represented by the inequality 1.5P + 2M ≤ 20.

Explanation:

The question asks for an inequality that represents the possible values for the number of peaches (P) and mangos (M) Marques and his children can purchase at a grocery store, given each peach costs $1.50, and each mango costs $2. When given a budget constraint, we use the budget constraint equation which is structured as P₁ × Q₁ + P₂ × Q₂ ≤ Budget, where P is the price of an item, Q is the quantity of the item, and Budget is the total amount of money one has to spend. In Marques' case, assuming they have $20 to spend, the inequality would be 1.5P + 2M ≤ 20, where 1.5 represents the cost of a peach and 2 represents the cost of a mango.

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