Jasmine plans to make and sell birdhouses this summer to earn extra money. She bought some woodworking tools for $286, and she will need to buy $12 worth of wood for each birdhouse. She plans to sell the birdhouses for $25 each.

Question

How many birdhouses must Jasmine sell so that her sales equal the cost of the wood and tools?
birdhouses

Answer 1

To determine how many birdhouses Jasmine needs to sell to cover her costs, we first need to set up an equation based on her expenses and income.

Costs:

• Initial tool cost: $286
• Wood cost per birdhouse: $12

Let's denote the number of birdhouses Jasmine sells as \( x \). Then, her total costs for \( x \) birdhouses can be expressed as: \[ \text{Total Cost} = 286 + 12x \]

Income:

• Selling price per birdhouse: $25

The income from selling \( x \) birdhouses can be expressed as: \[ \text{Total Income} = 25x \]

We want her total income to equal her total costs: \[ 25x = 286 + 12x \]

Now, let's solve for \( x \):

1. Subtract \( 12x \) from both sides: \[ 25x - 12x = 286 \] \[ 13x = 286 \]

2. Divide both sides by 13: \[ x = \frac{286}{13} \] \[ x = 22 \]

Jasmine must sell 22 birdhouses to cover the costs of her tools and wood.