Gabriella and her children went into a grocery store and where they sell apples for $1 each and mangos for $0.50 each. Gabriella has $15 to spend and must buy at least 19 apples and mangos altogether. If Gabriella decided to buy 13 mangos, determine the maximum number of apples that she could buy. If there are no possible solutions, submit an empty answer.

She can buy a maximum of 8 apples.

Step-by-step explanation:

Let x represent the number of apples that she wants to buy.

The grocery store sells apples for $1 each and mangos for $0.50 each.

If Gabriella decided to buy 13 mangos, it means that the cost of buying x apples and 13 mangoes is expressed as

x + 13 × 0.5 = x + 6.5

If she buy at least 19 apples, it means that

x + 13 ≥ 19

x ≥ 19 - 13

x ≥ 6

Gabriella has $15 to spend. It means that

x + 6.5 ≤ 15

x ≤ 15 - 6.5

x ≤ 8.5

Therefore, the maximum number of apples that she can buy is 8