Question

Damian and his children went into a grocery store where they sell apples for $1.75 each and mangos for $1.25 each. Damian has $20 to spend and must buy a minimum of 13 apples and mangos altogether. Let x represent the number of apples and y represent the number of mangos. Determine how many apples and mangos Damian can buy within his budget while satisfying the minimum purchase requirement.

Answer 1

To find out how many apples and mangos Damian can buy within his budget while satisfying the minimum purchase requirement, we can set up a system of inequalities and graph the feasible region.

Step-by-step explanation:

To find out how many apples and mangoes Damian can buy within his budget while satisfying the minimum purchase requirement, we can set up a system of inequalities.

Let x represent the number of apples and y represent the number of mangoes. The cost of each apple is $1.75, so the cost of x apples is 1.75x. The cost of each mango is $1.25, so the cost of y mangos is 1.25y.

We are given that Damian has $20, so the total cost of the apples and mangos must be less than or equal to $20: 1.75x + 1.25y ≤ 20.

We are also given that Damian must buy a minimum of 13 apples and mangos altogether: x + y ≥ 13.

Using these two inequalities and the constraints, we can graph the feasible region and find the number of apples and mangos Damian can buy within his budget while satisfying the minimum purchase requirement.

Answer 2

To determine the number of apples and mangos Damian can buy, we must consider the price of each and the $20 budget. With prices at $1.75 for apples and $1.25 for mangos, inequalities can be solved to find the maximum possible number he can purchase while satisfying the minimum requirement of 13 fruits.

Step-by-step explanation:

To determine how many apples and mangos Damian can buy within his budget of $20 while satisfying the minimum purchase requirement of 13 fruits, we need to set up two inequalities based on the given prices: $1.75 per apple and $1.25 per mango. Let x represent the number of apples and y represent the number of mangos.

The total cost equation is 1.75x + 1.25y ≤ $20.

The minimum purchase requirement is x + y ≥ 13.

To find out how many of each fruit he can purchase, we will look at the most he can spend on each type of fruit without exceeding the $20:

For apples: 1.75x ≤ $20, giving us a maximum of x ≤ 11 (since 11 * $1.75 = $19.25).

For mangos: 1.25y ≤ $20, allowing for a maximum of y ≤ 16 (since 16 * $1.25 = $20).

However, he must buy at least 13 fruits in total. If he buys the maximum 11 apples, he can only afford one more mango ($0.75 remaining), which does not meet the minimum requirement of 13 fruits. By trying different combinations that satisfy both the budget and minimum number of fruits, Damian can find the appropriate number of apples and mangos to buy.