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Lena sells earrings from a booth at the arts fair. She pays $200 to rent the booth. She makes $5 from each pair of earrings she sells.

Her profit, P, can be found using the following equation, where n is the number of pairs of earrings sold.
(2 points)

Write an equation:
How many pairs of earrings must Lena sell to earn a profit of $450?
pairs.

1 answer

To find the profit \( P \) for Lena, we can set up the equation based on her costs and earnings. The total profit \( P \) can be calculated using the formula:

\[ P = 5n - 200 \]

where:

  • \( P \) is the profit,
  • \( n \) is the number of pairs of earrings sold,
  • \( 5n \) is the total money made from selling \( n \) pairs of earrings,
  • \( 200 \) is the cost of renting the booth.

Now, to find how many pairs of earrings (\( n \)) Lena must sell to earn a profit of $450, we set \( P \) to 450:

\[ 450 = 5n - 200 \]

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

  1. Add 200 to both sides:

\[ 450 + 200 = 5n \]

\[ 650 = 5n \]

  1. Divide both sides by 5:

\[ n = \frac{650}{5} \]

\[ n = 130 \]

Lena must sell 130 pairs of earrings to earn a profit of $450.