Elise will be selling her handmade jewelry at a craft fair this weekend. She plans to sell each necklace for $28 and each bracelet for $22. After covering the $110 she spent on supplies, Elise hopes to earn a profit of at least $400.
If n represents the number of necklaces sold and b represents the number of bracelets sold, which inequality describes this situation?
a) 28n +22b +110 < or equal to 400
b)28n +22b +110 > or equal to 400
c) 28n + 22b - 110 > or equal to 400
d) 28n + 22b - 110 < or equal to 400
If Elise sells 12 necklaces, what is the minimum number of bracelets she needs to sell to earn a profit of $400 or more?
bracelets
To determine the inequality that describes Elise's situation, we can start with the equation for profit:
Profit = Total Sales - Total Costs
Profit = (28n + 22b) - 110
We want Elise to earn a profit of at least $400, so we set up the inequality:
Profit >= 400
(28n + 22b) - 110 >= 400
28n + 22b >= 510
Therefore, the correct inequality that describes the situation is:
b >= (510 - 28n) / 22
If Elise sells 12 necklaces (n = 12), we substitute n = 12 into the inequality above:
b >= (510 - 28*12) / 22
b >= (510 - 336) / 22
b >= 174 / 22
b >= 7.9
Since Elise can only sell whole numbers of bracelets, she would need to sell at least 8 bracelets to earn a profit of $400 or more.