At a certain real estate firm,realtors selling homes receive a commission of 7% for the first 140,000 of the selling price, and 5% for any amount exceeding 140,000. A realtor for the firm received 11,350 for selling a house. What was its selling price?

Let X be the selling price

11,350 = 0.07*140,000 + 0.05 (X - 140,000)
= 9,800 + 0.05 X - 7,000
= 2,800 + 0.05 X
0.05 X = 11,350 - 2,800 = 8,550
Finish by completing the last step.

Well, it seems like this real estate firm is rewarding their realtors with some serious commission! Let's solve this mystery.

First, let's assume the selling price of the house is "x".

According to the given information, the realtor receives a 7% commission on the first $140,000 of the selling price. That means the realtor earned 0.07 * $140,000 = $9,800 for this portion.

Now, the remaining amount above $140,000 (x - $140,000) will be subject to a 5% commission, so the realtor earned 0.05 * (x - $140,000).

Adding these two amounts together, we can set up the equation:
$9,800 + 0.05 * (x - $140,000) = $11,350

Now, let's solve this equation and find out the selling price!

9,800 + 0.05x - 0.05($140,000) = $11,350

9,800 + 0.05x - 0.05 * $140,000 = $11,350

Simplifying, we get:

9,800 + 0.05x - $7,000 = $11,350

0.05x = $11,350 - $9,800 + $7,000

0.05x = $8,550

x = $8,550 / 0.05

x = $171,000

So, the selling price of the house was $171,000. Keep in mind that this calculation assumes the realtor received the full commission without any deductions or taxes.

To find out the selling price of the house, we can break down the commission received by the realtor into the two tiers: 7% for the first $140,000 and 5% for any amount exceeding $140,000.

Let's assume the selling price of the house is "x".

The realtor received a commission of 7% for the first $140,000, which is ($140,000) * (7/100) = $9,800.

For the amount exceeding $140,000, the commission rate is 5%. So, the commission for the remaining amount (x - $140,000) is (x - $140,000) * (5/100).

The total commission received by the realtor, including both tiers, is $11,350.

Therefore, the equation for the total commission received by the realtor is:

$9,800 + (x - $140,000) * (5/100) = $11,350.

Now, we will solve this equation to find the selling price "x". Here are the steps:

Step 1: Distribute the (5/100) term:
$9,800 + (5/100)(x - $140,000) = $11,350.

Step 2: Simplify the equation:
$9,800 + (x - $140,000)(5/100) = $11,350.

Step 3: Multiply 5/100 by (x - $140,000):
$9,800 + (5/100)x - (5/100)($140,000) = $11,350.

Step 4: Simplify the equation further:
$9,800 + (5/100)x - ($7,000) = $11,350.

Step 5: Combine like terms:
(5/100)x + $9,800 - $7,000 = $11,350.

Step 6: Simplify and solve for "x":
(5/100)x = $11,350 - $9,800 + $7,000,
(5/100)x = $1,550 + $7,000,
(5/100)x = $8,550.

Step 7: Multiply both sides by 100/5 to isolate "x":
x = ($8,550) * (100/5).

Step 8: Calculate the value of "x":
x = $171,000.

Therefore, the selling price of the house is $171,000.

To find the selling price of the house, we need to determine two things: the portion of the selling price that is subject to a 7% commission and the portion that is subject to a 5% commission.

Let's assume the selling price of the house is "x".

First, we need to find the commission for the amount up to $140,000. Since this portion is eligible for a 7% commission, the commission earned from this portion can be calculated as 7% of $140,000, which is (7/100) * $140,000 = $9,800.

Next, we need to find the commission for the amount exceeding $140,000. The difference between the selling price and $140,000 is denoted as (x - $140,000). The commission earned from this portion can be calculated as 5% of (x - $140,000), which is (5/100) * (x - $140,000).

The total commission earned by the realtor is given as $11,350. Therefore, we can set up the equation:

$9,800 + (5/100) * (x - $140,000) = $11,350

Simplifying the equation:

($5/100) * (x - $140,000) = $11,350 - $9,800

($5/100) * (x - $140,000) = $1,550

Now, let's solve for (x - $140,000):

(x - $140,000) = ($1,550 * 100) / $5

(x - $140,000) = 31,000

Finally, let's find the selling price of the house:

x = 31,000 + $140,000

x = $171,000

Therefore, the selling price of the house is $171,000.