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. Graph your solution on the number line below
Let's denote the discount as $x. Since each box usually costs $7 and there are 9 boxes, the total cost without any discount would be 7*9 = $<<7*9=63>>63.
To stay within the budget of $36, the discounted cost must be less than or equal to $36. Therefore, we can write the inequality as:
63 - x ≤ 36
To solve for x, we can subtract 63 from both sides of the inequality:
63 - x - 63 ≤ 36 - 63
-x ≤ -27
To isolate x, we can multiply both sides by -1 and reverse the inequality:
x ≥ 27
The granola bars could be discounted by $27 or more in order for the teacher to stay within his budget.
Graphing on the number line:
We will represent the inequality on a number line with a filled in circle at 27 (since it is greater than or equal to) and a right arrow extending to infinity on the number line.
Here is the visual representation:
<------------------------------------|----------------->
27 ⟷ ∞