Sure, let's go through each part of the problem step-by-step:
### Question 14: If she buys two bales, what will her total amount of costs be?
To determine the total cost when she buys two bales, we need to calculate the cost of jackets and coats separately and then sum them up. Given:
- Each bale contains 33 jackets and 18 coats.
- The cost per jacket is \[tex]$8.
- The cost per coat is \$[/tex]14.
- She buys 2 bales.
For jackets:
- Total number of jackets in 2 bales = 33 jackets/bale 2 bales = 66 jackets.
- Total cost of jackets = 66 jackets \[tex]$8/jacket = \$[/tex]528.
For coats:
- Total number of coats in 2 bales = 18 coats/bale 2 bales = 36 coats.
- Total cost of coats = 36 coats \[tex]$14/coat = \$[/tex]504.
The total cost for 2 bales:
- Total cost = \[tex]$528 (jackets) + \$[/tex]504 (coats) = \[tex]$1032.
### Question 15: Assume that the number of jackets and coats doubles, calculate her sales and profit.
Given that the quantity of jackets and coats doubles:
- Original total jackets = 66 (from 2 bales), so doubled total jackets = 66 jackets * 2 = 132 jackets.
- Original total coats = 36 (from 2 bales), so doubled total coats = 36 coats * 2 = 72 coats.
The sales prices are:
- Sales price per jacket = \$[/tex]25.
- Sales price per coat = \[tex]$45.
Calculate total sales:
- Sales from jackets = 132 jackets * \$[/tex]25/jacket = \[tex]$3300.
- Sales from coats = 72 coats * \$[/tex]45/coat = \[tex]$3240.
- Doubled total sales = \$[/tex]3300 (jackets) + \[tex]$3240 (coats) = \$[/tex]6540.
Given the original total cost for 2 bales is \[tex]$1032:
- Doubled profit = Doubled total sales - Total cost.
- Doubled profit = \$[/tex]6540 - \[tex]$1032 = \$[/tex]5508.
### Summary Table
To understand her costs and sales, let's create a table where the number of items and prices increase proportionally:
| Item | Quantity (Original) | Quantity (Doubled) | Cost per Item | Total Cost (Original) | Total Cost (Doubled) | Selling Price per Item | Total Sales (Original) | Total Sales (Doubled) |
|------------|---------------------|--------------------|---------------|----------------------|----------------------|------------------------|------------------------|------------------------|
| Jackets | 66 | 132 | \[tex]$8 | \$[/tex]528 | \[tex]$528 | \$[/tex]25 | \[tex]$1650 | \$[/tex]3300 |
| Coats | 36 | 72 | \[tex]$14 | \$[/tex]504 | \[tex]$504 | \$[/tex]45 | \[tex]$1620 | \$[/tex]3240 |
| Total Cost: | \[tex]$1032 | | |
| Total Sales: | \$[/tex]3270 | \[tex]$6540 | |
| Profit: | \$[/tex]2238 | \$5508 | |
Thus, the total cost, original profit, doubled total sales, and doubled profit are clearly outlined and verified.
