what does it cost? solve this problem: a warehouse sells clothing at a fraction of its original cost. the…
what does it cost? solve this problem: a warehouse sells clothing at a fraction of its original cost. the table below shows the fraction off the original prices for clothing that remains in the warehouse after 10 days, 20 days, and 30 days. warehouse prices\n| item | price | after 10 days | after 20 days | after 30 days |\n| ---- | ---- | ---- | ---- | ---- |\n| jacket | $120 | 1/4 off | 1/3 off | 1/2 off |\n| shoes | $40 | 1/5 off | 2/5 off | 3/5 off |\n| shirt | $12 | 1/4 off | 1/3 off | 2/3 off |\n- find the price of the items after each 10 - day period to complete the chart below. write a numerical expression to show how you arrived at each solution. warehouse prices\n| item | price | after 10 days | after 20 days | after 30 days |\n| ---- | ---- | ---- | ---- | ---- |\n| jacket | $120 | | | |\n| shoes | $40 | | | |\n| shirt | $12 | | | |\nsuppose you have $100 to spend.\n2. within the range of $0.00 to $100.00, what are all possible combinations of items you might buy after 10 days?\n3. would you have enough money to buy 2 jackets after 20 days? justify your solution.
Answer
Explanation:
Step1: Calculate price of jacket after 10 days
The discount is $\frac{1}{4}$ off. So the price is $120\times(1 - \frac{1}{4})=120\times\frac{3}{4}=90$.
Step2: Calculate price of jacket after 20 days
The discount is $\frac{1}{3}$ off. So the price is $120\times(1 - \frac{1}{3})=120\times\frac{2}{3}=80$.
Step3: Calculate price of jacket after 30 days
The discount is $\frac{1}{2}$ off. So the price is $120\times(1 - \frac{1}{2})=120\times\frac{1}{2}=60$.
Step4: Calculate price of shoes after 10 days
The discount is $\frac{1}{5}$ off. So the price is $40\times(1 - \frac{1}{5})=40\times\frac{4}{5}=32$.
Step5: Calculate price of shoes after 20 days
The discount is $\frac{2}{5}$ off. So the price is $40\times(1 - \frac{2}{5})=40\times\frac{3}{5}=24$.
Step6: Calculate price of shoes after 30 days
The discount is $\frac{3}{5}$ off. So the price is $40\times(1 - \frac{3}{5})=40\times\frac{2}{5}=16$.
Step7: Calculate price of shirt after 10 days
The discount is $\frac{1}{4}$ off. So the price is $12\times(1 - \frac{1}{4})=12\times\frac{3}{4}=9$.
Step8: Calculate price of shirt after 20 days
The discount is $\frac{1}{3}$ off. So the price is $12\times(1 - \frac{1}{3})=12\times\frac{2}{3}=8$.
Step9: Calculate price of shirt after 30 days
The discount is $\frac{2}{3}$ off. So the price is $12\times(1 - \frac{2}{3})=12\times\frac{1}{3}=4$.
The completed table:
| ITEM | PRICE | AFTER 10 DAYS | AFTER 20 DAYS | AFTER 30 DAYS |
|---|---|---|---|---|
| Jacket | $120 | $90 | $80 | $60 |
| Shoes | $40 | $32 | $24 | $16 |
| Shirt | $12 | $9 | $8 | $4 |
2.
We consider combinations of items with prices after 10 - days in the range of $80 - 100$.
- One jacket ($90$)
- One jacket ($90$) and one shirt ($9$) total is $90 + 9=99$
3.
The price of one jacket after 20 days is $80$. The price of 2 jackets is $2\times80 = 160$. Since we have only $100$, we do not have enough money to buy 2 jackets after 20 days.
Answer:
| ITEM | PRICE | AFTER 10 DAYS | AFTER 20 DAYS | AFTER 30 DAYS |
|---|---|---|---|---|
| Jacket | $120 | $90 | $80 | $60 |
| Shoes | $40 | $32 | $24 | $16 |
| Shirt | $12 | $9 | $8 | $4 |
- Possible combinations: One jacket; One jacket and one shirt
- No, because the cost of 2 jackets after 20 days is $160$ and we have only $100$.