A company charges $20 to make one monogrammed shirt, but reduces this cost by $0.10 per shirt for each additional shirt ordered up to 100 shirts. If the cost of an
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Problem:**
A company charges $20 to make one monogrammed shirt, but reduces this cost by $0.10 per shirt for each additional shirt ordered up to 100 shirts. If the cost of an order is $846, how many shirts were ordered?
**Solution:**
If the cost of an order is $846, \(\square\) shirts were ordered. (Simplify your answer.)
**Explanation:**
Let \( x \) be the number of shirts ordered. The price per shirt decreases by $0.10 for each additional shirt, starting at $20 up to the first 100 shirts.
- The cost per shirt when ordering \( x \) shirts is \( 20 - 0.10(x - 1) \).
- The total cost for \( x \) shirts is:
\[
x \times (20 - 0.10(x - 1)) = 846
\]
**Steps to Solve:**
1. Expand and simplify the equation:
\[
x \times (20 - 0.10x + 0.10) = 846
\]
\[
20x - 0.10x^2 + 0.10x = 846
\]
2. Combine like terms:
\[
-0.10x^2 + 20.1x = 846
\]
3. Rearrange into a standard quadratic equation:
\[
0.10x^2 - 20.1x + 846 = 0
\]
4. Use the quadratic formula to solve for \( x \):
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
where \( a = 0.10 \), \( b = -20.1 \), \( c = 846 \).
5. Calculate the discriminant and solve for \( x \).
Finally, assess \( x \) to ensure it is a realistic number of shirts (a positive integer not exceeding 100 for a valid scenario given the condition of price reduction).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb95e33bb-c8fe-4d5f-9d28-351192aa0ecf%2F5cfdef00-5396-419a-bc0d-905d67cead7c%2Fppf7be_processed.jpeg&w=3840&q=75)
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