To determine how many pounds of peaches Rammy can buy within his budget of [tex]$9.60, we need to solve the given inequality:
\[ 1.20x + 3.60 \leq 9.60 \]
Let’s solve this step-by-step:
1. Isolate the term involving \( x \):
Start by subtracting the cost of the milk ($[/tex]3.60) from both sides of the inequality to isolate the term involving the peaches:
[tex]\[ 1.20x + 3.60 - 3.60 \leq 9.60 - 3.60 \][/tex]
Simplifies to:
[tex]\[ 1.20x \leq 6.00 \][/tex]
2. Solve for [tex]\( x \)[/tex]:
Next, divide both sides by the coefficient of [tex]\( x \)[/tex] (which is $1.20) to solve for [tex]\( x \)[/tex]:
[tex]\[ x \leq \frac{6.00}{1.20} \][/tex]
Simplifies to:
[tex]\[ x \leq 5 \][/tex]
Therefore, Rammy can buy 5 pounds or less of peaches. The number of pounds of peaches Rammy can buy is represented by option C.
So, the correct answer is:
C. [tex]\( x \leq 5 \)[/tex]; Rammy can buy 5 pounds or less of peaches.
