Question

Mongo wants to buy mangoes and avocados at a farmer’s market. His famous mango/avocado salad requires that he buys at least 12 of these fruits. If each mango is $2.50 each and each avocado is $3.50 each and he has a total of $45 to spend, find all combinations of fruit items that Mongo can buy.

Answer 1

To determine the combinations of mangoes and avocados that Mongo can buy, use inequalities based on the constraints of at least 12 fruits and a budget of $45. Calculate combinations by incrementing the number of avocados and solving for mangoes, ensuring whole numbers for both fruits.

Step-by-step explanation:

To find all possible combinations of mangoes and avocados that Mongo can buy, we need to consider the constraints: Mongo has to buy at least 12 fruits and cannot spend more than $45. Let's denote the number of mangoes as m and avocados as a. The price per mango is $2.50, and the price per avocado is $3.50.

With this information, we can set up two inequalities:

1. m + a ≥ 12 (at least 12 fruits)
2. 2.50m + 3.50a ≤ $45 (total cost not exceeding $45)

Now let's solve for allowable combinations. We can rewrite the second inequality to solve for m:

m ≤ (45 - 3.50a)/2.50

Considering that Mongo cannot buy a fraction of a fruit, m and a must also be whole numbers. Starting with a=0 and incrementing, we can find combinations such as (18 mangoes, 0 avocados), (12 mangoes, 3 avocados), and so on up until the combination that exhausts Mongo's budget or exceeds the minimum number of fruits required.