A budget inequality describes purchase combinations that stay within a spending limit. Multiply each item's price by the letter that counts it, then add the costs. The phrase at most means the total can be below the budget or exactly equal to it. Watch for prices paired with the wrong letters.
Hints
- Hint 1
A price per item must be multiplied by the number of those items. Which letter counts bottles, and which counts backpacks?
- Hint 2
Both kinds of items cost money, so the total is the sum of their separate costs. What expression gives that total?
- Hint 3
An inequality compares amounts that need not be equal. At most allows spending less than the budget or exactly the budget. Which symbol includes both cases?
Step-by-step
Build the budget inequality
Step 1Match each price to its count
No Desmos needed. You're translating prices and a budget, not evaluating a given expression. Each bottle costs $9 and counts bottles, so the bottles cost . Each backpack costs $24 and counts backpacks, so the backpacks cost . Keep each price with its own letter.
- Step 2
Add the two costs
The club pays for both types of items, so add their costs to get the total:
Don't subtract the backpack cost. Buying a backpack can't lower the bill.
- Step 3
Apply the budget limit
At most $300 means the total can be less than or equal to $300, so the inequality is
The bar in includes spending exactly $300. With and as nonnegative whole-number counts, this represents the combinations the club can afford. Choice D.