The cost of operating an ice cream stand is described by the function C(q)=897+1.35q
  dollars when q
 ice cream cones are produced.

Each ice cream cone sells for $4.98.

What quantity of ice cream cones must the stand sell to break even?

Round your answer to the nearest whole number. 

The break-even point occurs when the total revenue equals the total cost.

1. **Revenue Function**: The revenue from selling $ q $ ice cream cones is given by:
   \[
   R(q) = 4.98q
   \]
   since each ice cream cone sells for $4.98.

2. **Cost Function**: The cost of producing $ q $ ice cream cones is given by:
   \[
   C(q) = 897 + 1.35q
   \]
   where $897 is the fixed cost and $1.35 is the variable cost per cone.

3. **Break-Even Condition**: To break even, the total revenue must equal the total cost:
   \[
   R(q) = C(q)
   \]
   Substituting the expressions for $ R(q) $ and $ C(q) $:
   \[
   4.98q = 897 + 1.35q
   \]

4. **Solve for $ q $**:
   \[
   4.98q - 1.35q = 897
   \]
   \[
   3.63q = 897
   \]
   \[
   q = \frac{897}{3.63} \approx 247.11
   \]

   Rounding to the nearest whole number, the ice cream stand must sell **247 ice cream cones** to break even.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. How much profit does the stand make if they sell 300 ice cream cones?
2. What is the total cost to produce 500 ice cream cones?
3. What is the revenue from selling 600 ice cream cones?
4. How does the break-even point change if the cost per cone increases to $1.50?
5. What is the new break-even point if the fixed cost is reduced to $850?

**Tip**: When solving break-even problems, always equate total cost to total revenue and solve for the quantity!

The cost of operating an ice cream stand is described by the function C(q) = 897 + 1.35q dollars when q ice cream cones are produced. Each ice cream cone sells for $4.98. What quantity of ice cream cones must the stand sell to break even? Round your answer to the nearest whole number.

Discover how to calculate the break-even point for an ice cream stand using linear equations. Learn how to equate the cost and revenue functions and solve for the quantity of cones needed to break even. In this example, the stand must sell 247 cones. Suitable for students in Grades 8-10.

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