Question
Jana and Tim both sell cleaning products to local housecleaning services. When Jana orders from the manufacturer of the products she sells, she is given a 15% discount on her total purchase, and she must pay a $15 shipping fee. Each of Tim’s orders to his manufacturer is charged at 85% of the full purchase price of the products, and he pays a $4 handling fee, plus $11 for shipping.
Which statements are true? Select two that apply.
A.
Jana and Tim will only spend the same amount on purchase orders to their manufacturers when they each order products with a total purchase value of $100.
B.
Jana and Tim will never spend exactly the same amount on purchase orders to their manufacturers.
C.
When Jana and Tim purchase products having the same total value, their costs for the purchases will be the same.
D.
If Jana switches to Tim’s manufacturer for her product purchases, her cost will decrease.
E.
If Tim switches to Jana’s manufacturer for his product purchases, his cost will remain the same.
Which statements are true? Select two that apply.
A.
Jana and Tim will only spend the same amount on purchase orders to their manufacturers when they each order products with a total purchase value of $100.
B.
Jana and Tim will never spend exactly the same amount on purchase orders to their manufacturers.
C.
When Jana and Tim purchase products having the same total value, their costs for the purchases will be the same.
D.
If Jana switches to Tim’s manufacturer for her product purchases, her cost will decrease.
E.
If Tim switches to Jana’s manufacturer for his product purchases, his cost will remain the same.
Answers
GPT-4o mini
To determine which statements are true, we need to analyze the costs that Jana and Tim incur when they order cleaning products.
**Jana's Cost Calculation:**
- Total purchase value (x)
- Discount: 15% of x → she pays 85% of x (0.85x)
- Shipping fee: $15
- Total cost for Jana: \( \text{Total Cost} = 0.85x + 15 \)
**Tim's Cost Calculation:**
- Total purchase value (x)
- Discount: 15% (similar to Jana), but Tim pays 85% of the full purchase price, so he pays 85% of x (0.85x)
- Handling fee: $4
- Shipping fee: $11
- Total cost for Tim: \( \text{Total Cost} = 0.85x + 4 + 11 \) = \( 0.85x + 15 \)
Now we can compare their costs:
1. **Total Cost for Jana**: \( 0.85x + 15 \)
2. **Total Cost for Tim**: \( 0.85x + 15 \)
From this, we can see clearly that Jana's and Tim's total costs are the same for any total purchase value (x) because both expressions simplify to the same form.
Now let's evaluate the statements based on the analysis:
A. **False** - Jana and Tim will spend the same amount at any order amount, not just when the total purchase value is $100.
B. **False** - Since their costs are the same for any order size, they can spend the same amount on their orders.
C. **True** - When Jana and Tim purchase products having the same total value, their costs will be the same (both cost expressions are equal).
D. **False** - If Jana switches to Tim’s manufacturer, her cost remains the same because Tim's total cost formula is equivalent to hers.
E. **False** - If Tim switches to Jana's manufacturer, his total cost also remains the same since the calculation for both is the same.
The two true statements are:
- **C. When Jana and Tim purchase products having the same total value, their costs for the purchases will be the same.**
Thus, the answer is **C** is true (only one true statement found).
**Jana's Cost Calculation:**
- Total purchase value (x)
- Discount: 15% of x → she pays 85% of x (0.85x)
- Shipping fee: $15
- Total cost for Jana: \( \text{Total Cost} = 0.85x + 15 \)
**Tim's Cost Calculation:**
- Total purchase value (x)
- Discount: 15% (similar to Jana), but Tim pays 85% of the full purchase price, so he pays 85% of x (0.85x)
- Handling fee: $4
- Shipping fee: $11
- Total cost for Tim: \( \text{Total Cost} = 0.85x + 4 + 11 \) = \( 0.85x + 15 \)
Now we can compare their costs:
1. **Total Cost for Jana**: \( 0.85x + 15 \)
2. **Total Cost for Tim**: \( 0.85x + 15 \)
From this, we can see clearly that Jana's and Tim's total costs are the same for any total purchase value (x) because both expressions simplify to the same form.
Now let's evaluate the statements based on the analysis:
A. **False** - Jana and Tim will spend the same amount at any order amount, not just when the total purchase value is $100.
B. **False** - Since their costs are the same for any order size, they can spend the same amount on their orders.
C. **True** - When Jana and Tim purchase products having the same total value, their costs will be the same (both cost expressions are equal).
D. **False** - If Jana switches to Tim’s manufacturer, her cost remains the same because Tim's total cost formula is equivalent to hers.
E. **False** - If Tim switches to Jana's manufacturer, his total cost also remains the same since the calculation for both is the same.
The two true statements are:
- **C. When Jana and Tim purchase products having the same total value, their costs for the purchases will be the same.**
Thus, the answer is **C** is true (only one true statement found).