A caterer has a budget of $1,200 for appetizers. Before ordering any food, the caterer must pay a $60 service fee. Mini sandwiches cost $3 each, and stuffed mushrooms cost $5 each.
Which inequality represents the possible numbers of mini sandwiches, , and stuffed mushrooms, , the caterer can order without exceeding the budget?
A two-variable inequality describes which combinations of two items fit a limit. For a budget question, match each count to its price and account for any fixed fee paid before the items are bought. Subtract that fee from the budget, then compare the items’ total cost with the amount left. The trap is giving the items the full budget.
Hints
- Hint 1
A fixed fee is paid once, no matter how many appetizers are ordered. It uses part of the overall budget before the food is bought. How much money remains for sandwiches and mushrooms?
- Hint 2
Each variable stands for a count: counts sandwiches and counts mushrooms. Multiply each count by its own price, then add the two costs. What expression gives the total food cost?
- Hint 3
At most means the cost may reach the limit but cannot go above it. Spending exactly the amount left is allowed. Which inequality sign includes that possibility?
Step-by-step
Subtract the fee, then model the food cost
Step 1Find the money left for food
No Desmos needed. This takes one subtraction and a direct translation of the budget. The service fee is paid before any food, so subtract it from the $1,200 budget:
A fixed fee uses part of the budget before any per-item costs are added.
- Step 2
Write the total food cost
The mini sandwiches cost $3 each, so they cost . The stuffed mushrooms cost $5 each, so they cost . Add the prices matched to their counts to get the food cost:
- Step 3
Set the budget limit
“Without exceeding” means the food cost can be no more than the $1,140 left. Use less than or equal to, , because spending exactly that amount is allowed:
This represents the possible numbers of appetizers. Choice C.