9 A teacher wants to buy 9 boxes of granola bars for a school trip. ● Each box usually costs $7, but many grocery stores are having a sale on granola bars this week, and different stores are selling boxes of granola bars at different discounts. ● This teacher can spend at most $36 on granola bars. Write and solve an inequality to represent the amount that the granola bars could be discounted so that this teacher can stay within his budget.
Let's say the discount for each box of granola bars is represented by the variable x. Since the teacher wants to buy 9 boxes of granola bars, the total amount spent can be calculated as 9 * (7 - x).
The teacher can spend at most $36, so we can write the following inequality:
9 * (7 - x) ≤ 36
To solve this inequality, we can start by simplifying the expression on the left side:
63 - 9x ≤ 36
Next, we can isolate the variable x by subtracting 63 from both sides:
-9x ≤ 36 - 63
-9x ≤ -27
Finally, we can divide both sides of the inequality by -9. Since dividing by a negative number reverses the inequality, we need to flip the inequality symbol:
x ≥ -27 / -9
x ≥ 3
Therefore, the granola bars can be discounted by at most $3 for the teacher to stay within his budget.