Question

jacket $120 after 10 days 1/4 off for jacket, 1/5 off for shoes, 1/4 off for shirt, and after 20 days 1/3 off for jacket, 2/5 off shoes, 1/3 for shirt off, and after 30 days 1/2 off for jacket, 3/5 off for shoes, 2/3 off for shirt.
shoes $40
shirt $12

Answer 1

To find the final prices of the jacket, shoes, and shirt after the specified discounts over time, let's calculate each one step by step.

### Initial Prices:
- Jacket: $120
- Shoes: $40
- Shirt: $12

### After 10 Days:
**Discounts:**
- Jacket: 1/4 off (25%)
- Shoes: 1/5 off (20%)
- Shirt: 1/4 off (25%)

**Calculations:**
1. Jacket price after 10 days:
\[
\text{Discount} = 120 \times \frac{1}{4} = 30
\]
\[
\text{New price} = 120 - 30 = 90
\]

2. Shoes price after 10 days:
\[
\text{Discount} = 40 \times \frac{1}{5} = 8
\]
\[
\text{New price} = 40 - 8 = 32
\]

3. Shirt price after 10 days:
\[
\text{Discount} = 12 \times \frac{1}{4} = 3
\]
\[
\text{New price} = 12 - 3 = 9
\]

### Prices after 10 Days:
- Jacket: $90
- Shoes: $32
- Shirt: $9

### After 20 Days:
**Discounts:**
- Jacket: 1/3 off (33.33%)
- Shoes: 2/5 off (40%)
- Shirt: 1/3 off (33.33%)

**Calculations:**
1. Jacket price after 20 days:
\[
\text{Discount} = 90 \times \frac{1}{3} = 30
\]
\[
\text{New price} = 90 - 30 = 60
\]

2. Shoes price after 20 days:
\[
\text{Discount} = 32 \times \frac{2}{5} = 12.8
\]
\[
\text{New price} = 32 - 12.8 = 19.2
\]

3. Shirt price after 20 days:
\[
\text{Discount} = 9 \times \frac{1}{3} = 3
\]
\[
\text{New price} = 9 - 3 = 6
\]

### Prices after 20 Days:
- Jacket: $60
- Shoes: $19.20
- Shirt: $6

### After 30 Days:
**Discounts:**
- Jacket: 1/2 off (50%)
- Shoes: 3/5 off (60%)
- Shirt: 2/3 off (66.67%)

**Calculations:**
1. Jacket price after 30 days:
\[
\text{Discount} = 60 \times \frac{1}{2} = 30
\]
\[
\text{New price} = 60 - 30 = 30
\]

2. Shoes price after 30 days:
\[
\text{Discount} = 19.2 \times \frac{3}{5} = 11.52
\]
\[
\text{New price} = 19.2 - 11.52 = 7.68
\]

3. Shirt price after 30 days:
\[
\text{Discount} = 6 \times \frac{2}{3} = 4
\]
\[
\text{New price} = 6 - 4 = 2
\]

### Final Prices after 30 Days:
- Jacket: $30
- Shoes: $7.68
- Shirt: $2

### Summary of Final Prices:
- **Jacket:** $30
- **Shoes:** $7.68
- **Shirt:** $2