Question

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.

Answer 1

To find Lena's profit, we can set up the equation based on her expenses and earnings.

Lena's profit \( P \) can be expressed with the equation:

\[
P = 5n - 200
\]

where:
- \( P \) is the profit,
- \( n \) is the number of pairs of earrings sold,
- \( 5n \) is the total earnings from selling \( n \) pairs of earrings ($5 for each pair),
- \( 200 \) is the booth rental cost.

To find out how many pairs of earrings she must sell to earn a profit of $450, we set \( P \) to 450 and solve for \( n \):

\[
450 = 5n - 200
\]

Now, add 200 to both sides:

\[
450 + 200 = 5n
\]

\[
650 = 5n
\]

Next, divide by 5:

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

\[
n = 130
\]

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