A two-variable linear inequality describes which pairs of item counts meet a limit. For sales, multiply each price by the number sold and add the earnings. Then translate at least as greater than or equal to, because reaching the goal exactly counts. Don't reverse the sign as though the goal were a spending limit.
Hints
- Hint 1
A rate is the amount earned for one item. To find the bracelet earnings, multiply the dollars per bracelet by the number of bracelets sold. How would you write that using ?
- Hint 2
The total revenue is all the money earned. Bracelets and hoodies both bring in money, so add their earnings rather than subtracting one from the other.
- Hint 3
At least means the club can reach the goal exactly or raise more. Which inequality symbol includes equality and points toward totals greater than the goal?
Step-by-step
Build the earnings inequality
Step 1Find the bracelet earnings
No Desmos needed. You're translating the fundraiser's words, not solving a given equation. A rate is the amount earned per item. At $12 per bracelet, selling bracelets brings in dollars.
- Step 2
Find the hoodie earnings
Each hoodie earns $20, so selling hoodies brings in dollars. The price multiplies the number sold, as it did for bracelets.
- Step 3
Add the two sources of money
Bracelets and hoodies both add to the money raised, so add their earnings to get the total revenue, or all the money earned:
- Step 4
Match the total to the goal
At least $600 includes exactly $600, so the total must be greater than or equal to the goal: . This represents the bracelet and hoodie counts that meet the fundraising goal. Choice D.