Keith and Dena Diem have personal property coverage with a​ $250 limit on​ currency, a​ $1,000 limit on​ jewelry, and a​ $2,500 limit on​ gold, silver, and pewter. They do not have a personal property floater. If ​$347 ​cash, ​$2 comma 548 of​ jewelry, and
​$1 comma 438 of pewterware were stolen from their​ home, what amount of loss would be covered by their​ homeowner's policy? If the​ Diems' deductible is ​$750​, how much will they receive on their​ claim?
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Part 1
The amount of loss covered by the​ Diems' homeowner's policy is ​$

enter your response here.  ​(Round to the nearest​ dollar.)
Part 2
If the​ Diems' deductible is ​$750​, the amount they will receive on their claim is ​$

enter your response here.  ​(Round to the nearest​ dollar.)

To solve this problem, we'll first calculate the amount of loss that would be covered by the Diems' homeowner's policy for each type of property, based on their policy limits. Then, we will calculate how much they will receive after applying the deductible.

### Part 1: Calculating the covered loss for each item

1. **Currency**:  
   The Diems' policy has a limit of $250 for currency. They lost $347 in cash, but the maximum amount the policy will cover is $250.  
   - Covered amount: **$250**

2. **Jewelry**:  
   The policy has a $1,000 limit for jewelry, but $2,548 worth of jewelry was stolen. Therefore, only $1,000 will be covered by the policy.  
   - Covered amount: **$1,000**

3. **Pewterware** (part of the $2,500 limit on gold, silver, and pewter):  
   They lost $1,438 worth of pewterware, which is below the $2,500 limit for this category, so the entire $1,438 is covered.  
   - Covered amount: **$1,438**

#### Total Covered Loss:
The total amount of loss covered by the policy is the sum of these covered amounts:
\[
\text{Total Covered Loss} = 250 + 1,000 + 1,438 = 2,688
\]

### Part 2: Applying the deductible
The Diems' deductible is $750, meaning that this amount will be subtracted from the total covered loss to determine the amount they will receive.

\[
\text{Amount they will receive} = \text{Total Covered Loss} - \text{Deductible}
\]
\[
\text{Amount they will receive} = 2,688 - 750 = 1,938
\]

### Final answers:
- **Part 1**: The total amount of loss covered by the Diems' homeowner's policy is **$2,688**.
- **Part 2**: After applying the deductible, the Diems will receive **$1,938** on their claim.

---

Do you want more details on how insurance limits or deductibles work?

Here are 5 follow-up questions:
1. What is the purpose of having policy limits in homeowner's insurance?
2. How do personal property floaters extend coverage for specific items?
3. What other types of property might have special limits in a typical homeowner's policy?
4. How does a deductible affect the cost of homeowner's insurance premiums?
5. What steps can be taken to increase coverage for valuable items like jewelry?

**Tip**: It's a good idea to review your insurance policy regularly to ensure it covers all of your valuables adequately!

Keith and Dena Diem have personal property coverage with a​ $250 limit on​ currency, a​ $1,000 limit on​ jewelry, and a​ $2,500 limit on​ gold, silver, and pewter. They do not have a personal property floater. If $347 cash, $2,548 of jewelry, and $1,438 of pewterware were stolen from their home, what amount of loss would be covered by their homeowner's policy? If the Diems' deductible is $750, how much will they receive on their claim?

This detailed solution shows how to calculate the payout for stolen items under a homeowner's policy, factoring in policy limits for cash, jewelry, and pewterware. Learn how to apply the deductible to the covered loss to determine the final amount received. Suitable for high school students studying real-world applications of arithmetic.

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