The soccer team is selling key chains to raise money for the team. They ordered 100 key chains that sell for .25 each. There is a flat shipping rate of $8. The team sells the key chains for $2 each. With that information, I figured they made $33.00 selling the 100 key chains, BUT
I don't know how to write an inequality to find the fewest number of key chains, k, the team must sell to make a profit (more than $33.
cost = 100(.25) + 8 = 33
number sold ---- x
2n - 33 > 0
2n > 33
n > 16.5 , so they sell at least 17 chains, or
the fewest number they must sell is 17
if they sold all 100, their profit is 200 - 33 or $167
Am I missing something here ? looks pretty straightforward.
To find the minimum number of key chains the team must sell to make a profit greater than $33, you can set up an inequality.
Let's break down the given information:
- The team ordered 100 key chains that sell for $0.25 each, which means the total cost of the key chains is 100 * $0.25 = $25.
- There is a flat shipping rate of $8.
- The team sells each key chain for $2.
To calculate the profit, we need to subtract the total cost from the total revenue:
Profit = Total Revenue - Total Cost.
The total revenue is the product of the selling price per key chain and the number of key chains sold, which can be represented as 2k, where k is the number of key chains sold.
The total cost is the sum of the cost of key chains and the flat shipping rate, which can be represented as $25 + $8 = $33.
So, the inequality to find the fewest number of key chains the team must sell to make a profit greater than $33 is:
2k - ($25 + $8) > $33.
Now, to solve this inequality for k, follow these steps:
1. Simplify the expression inside the parentheses:
2k - $33 > $33.
2. Combine like terms:
2k - $33 > $33.
3. Add $33 to both sides of the inequality:
2k > $33 + $33.
4. Simplify the right side:
2k > $66.
5. Divide both sides of the inequality by 2:
k > $66 / 2.
6. Simplify the right side:
k > $33.
Therefore, the fewest number of key chains the team must sell to make a profit greater than $33 is 34 key chains (since selling 33 key chains would result in a profit of exactly $33).
To find the fewest number of key chains the team must sell to make a profit, we can set up an inequality based on the given information.
Let's assume that the team must sell at least k key chains to make a profit. We know that each key chain sells for $2, so the total revenue from selling k key chains is 2k dollars.
The team ordered 100 key chains that sell for $0.25 each, so the total cost of the key chains is (100 * $0.25) = $25.
There is also a flat shipping rate of $8, which is a fixed cost that does not change based on the number of key chains sold.
Therefore, the total cost for the team is $25 + $8 = $33.
To make a profit, the revenue generated must be greater than the cost. So, we can write the inequality:
2k > $33
This inequality states that the revenue from selling the key chains (2k) must be greater than the total cost ($33).
Now, you can solve this inequality to find the fewest number of key chains (k) the team must sell to make a profit.