Kaelyn and her family went into a grocery store where they sell peaches for 1 each and mangos for 0.50 each. Kaelyn has 9 to spend and must buy at least 13 peaches and mangos altogether. Write a system of inequalities that could represent this situation. A ygeqslant -x+13 and x+0.5yleqslant 9 B yleqslant -x+13 and x+0.5yleqslant 9 C ygeqslant -x+13 and x+0.5ygeqslant 9 D yleqslant -x+13 and x+0.5ygeqslant 9

To represent the situation with a system of inequalities, we need to consider the constraints given in the problem.<br /><br />Let's define:<br />- \( x \) as the number of peaches Kaelyn buys.<br />- \( y \) as the number of mangos Kaelyn buys.<br /><br />Given constraints:<br />1. Kaelyn has $9 to spend.<br />2. The cost of each peach is $1.<br />3. The cost of each mango is $0.50.<br />4. Kaelyn must buy at least 13 peaches and mangos altogether.<br /><br />The total cost constraint can be written as:<br />\[ x + 0.5y \leq 9 \]<br /><br />The total number of fruits constraint can be written as:<br />\[ x + y \geq 13 \]<br /><br />Now, let's rewrite the second inequality in terms of \( y \):<br />\[ y \geq -x + 13 \]<br /><br />So the system of inequalities representing the situation is:<br />\[ y \geq -x + 13 \]<br />\[ x + 0.5y \leq 9 \]<br /><br />Therefore, the correct answer is:<br />A) \( y \geq -x + 13 \) and \( x + 0.5y \leq 9 \)