when leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. if the amount of the import tax that leo paid was $87.50, what was the total value of the item?

Let's analyze the problem step-by-step.

Problem Restatement

Leo imported an item and paid a 7% import tax only on the portion of the item's value exceeding $1,000. The total import tax he paid was $870. We need to find the total value of the item.

Step 1: Define Variables

Let:

• VVV = total value of the item (in dollars)
• The portion subject to tax = V−1000V-1000V−1000 (since tax applies only to the amount over $1,000)

Step 2: Write the Tax Equation

The tax paid is 7% of the portion over $1,000:

Tax=0.07×(V−1000)\text{Tax}=0.07\times (V-1000)Tax=0.07×(V−1000)

Given the tax paid is $870:

870=0.07×(V−1000)870=0.07\times (V-1000)870=0.07×(V−1000)

Step 3: Solve for VVV

V−1000=8700.07V-1000=\frac{870}{0.07}V−1000=0.07870​

Calculate:

8700.07=12428.57\frac{870}{0.07}=12428.570.07870​=12428.57

So,

V−1000=12428.57V-1000=12428.57V−1000=12428.57

V=12428.57+1000=13428.57V=12428.57+1000=13428.57V=12428.57+1000=13428.57

Final Answer:

The total value of the item was approximately $13,428.57. If you want, I can help you with more problems like this!