A clothing store ordered 300 sweaters and sold 20 of them at $100 the first week. The second week, the selling price was lowered by $10, and 40 sweaters were sold. In the third week. The selling price was lowered by another $10, and 60 sweated were sold. If the pattern continues,

Question

A clothing store ordered 300 sweaters and sold 20 of them at $100 the first week. The second week, the selling price was lowered by $10, and 40 sweaters were sold. In the third week. The selling price was lowered by another $10, and 60 sweated were sold. If the pattern continues,

A) how many weeks did it take to sell all sweaters?
B) what was the selling price in the final week?

For a) I started off by writing it out:
Number of sweaters each week: 300, 280, 240, 180

I got stuck because they don't reduce by a constant common ratio or common difference. How would you figure out this type of question?

Thanks in advance!

Answer 1

Week 1: 20 sweaters at $100 = $2000

Week 2: 40 sweaters at $90 = $3600
Week 3: 60 sweaters at $80 = $4800
Week 4: 80 sweaters at $70 = $5600
Week 5: 100 sweaters at $60 = $6000

100+80+60+40+20 = 300 sweaters sold in 5 weeks

A) Took 5 weeks
B) $60 a sweater in the final week

Answer 2

Ohhhh. Thank you ! I was going about it backwards!

Answer 3

Thanks for the answer

Answer 4

To solve this problem, you need to analyze the pattern and find a relationship between the number of sweaters sold and the selling price. Let's break it down step by step:

Step 1: Analyzing the first week:
- The store ordered 300 sweaters and sold 20 at $100 each.
- This means the store earned a total of 20 x $100 = $2000.

Step 2: Analyzing the second week:
- The selling price was lowered by $10, which means the sweaters were sold at $100 - $10 = $90 each.
- The store sold 40 sweaters, which means they earned 40 x $90 = $3600 in total.

Step 3: Analyzing the third week:
- The selling price was lowered by another $10, so the sweaters were sold at $90 - $10 = $80 each.
- The store sold 60 sweaters, earning 60 x $80 = $4800 in total.

From the above analysis, it appears that the total earnings each week are increasing. To find out how many weeks it took to sell all the sweaters, we need to determine the week where the total earnings exceeded or equaled the cost of all the sweaters.

Step 4: Calculating the total cost of the sweaters:
- The store ordered 300 sweaters.
- We don't have information on the purchase price of each sweater, so we'll assume they were sold at a price equal to the highest selling price, which is $100 in the first week.
- The total cost of all the sweaters would then be 300 x $100 = $30,000.

Step 5: Calculating the total earnings each week:
- Week 1: $2000
- Week 2: $3600
- Week 3: $4800

Now, let's figure out in which week the total earnings exceeded or equaled $30,000.

- Week 1: $2000
- Week 2: $2000 + $3600 = $5600
- Week 3: $5600 + $4800 = $10,400

Based on this pattern, you can see that it took more than three weeks to reach $30,000 in earnings. You can continue the pattern to find out exactly how many weeks it took.

For question B, the selling price in the final week is not clear from the given information. The pattern tells us that the selling price is reduced by $10 each week, but there is no specific selling price provided for the final week. To answer this question accurately, we need additional information or assumptions.