A small business owner has a budget of $2,200 to …

Business Questions
Short Answer
Step by Step Solution
Business Questions

A small business owner has a budget of $2,200 to purchase candles and must buy a minimum of 200 candles to maintain the discounted pricing. If small candles cost $4.90 each and large candles cost $11.60 each, what is the maximum number of large candles the owner can purchase while staying within the budget?

Short Answer

The maximum number of large candles the owner can purchase is determined by the equation 11.6 * x + 4.9 * (200 – x) = 2200. After simplifying and solving the equation, the result shows that the owner can buy up to 182 large candles within the budget.

Step-by-Step Solution

Step 1: Set Up the Equation

To find the maximum number of large candles the owner can purchase, start by establishing an equation based on the budget. The equation will include the cost of both large and small candles:

  • Let x be the number of large candles.
  • The equation is 11.6 * x + 4.9 * (200 – x) = 2200, where 200 is the total number of candles and 2200 is the total budget.

Step 2: Simplify the Equation

Next, simplify the equation to isolate x. Combine like terms to make calculations easier:

  • Distribute the 4.9: 11.6x + 980 – 4.9x = 2200.
  • Combine terms: This gives 6.7x + 980 = 2200.

Step 3: Solve for the Maximum Number of Candles

Finally, solve for x to find the maximum quantity of large candles that can be purchased within the budget:

  • Subtract 980 from both sides: 6.7x = 1220.
  • Divide by 6.7: x = 182.

This indicates that the owner can buy a maximum of 182 large candles to remain within the budget and retain the discounted pricing.

Related Concepts

Equation

A mathematical statement that asserts the equality of two expressions, typically containing variables and constants, used to model relationships in a problem.

Budget

The total amount of money allocated for purchasing items, which in this case limits the quantity that can be bought.

Candles

In this context, items being purchased, categorized into large and small, with given prices affecting the total budget constraints.

Table Of Contents
  1. A small business owner has a budget of $2,200 to purchase candles and must buy a minimum of 200 candles to maintain the discounted pricing. If small candles cost $4.90 each and large candles cost $11.60 each, what is the maximum number of large candles the owner can purchase while staying within the budget?

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