Let's break down the problem into its individual parts and solve each one step by step.
### Part 1: Quantity of Purple Sweet Potato Tarts
We are told that:
- The number of mixed fruit tarts is 147 less than the number of purple sweet potato tarts.
Let's denote the number of purple sweet potato tarts by [tex]\( P \)[/tex]. The number of mixed fruit tarts will then be [tex]\( P - 147 \)[/tex].
Thus, the number of purple sweet potato tarts is [tex]\( P \)[/tex].
### Part 2: Buffet Charges
We are given the following information about the buffet charges:
- The charge for a child is NT\[tex]$168.
- The charge for a child is NT\$[/tex]88 cheaper than the charge for an elderly person. Therefore, the charge for an elderly person is NT\[tex]$256.
\[
168 + 88 = 256
\]
- The charge for an adult is NT\$[/tex]143 higher than the charge for an elderly person. Therefore, the charge for an adult is NT\[tex]$399.
\[
256 + 143 = 399
\]
### Part 3: Total Butter Cookies
We are given the following information about the butter cookies:
- 353 butter cookies sold in the morning.
- 399 butter cookies sold in the afternoon.
- 48 butter cookies remaining unsold.
To find the total number of butter cookies, we sum the number sold in the morning, the number sold in the afternoon, and the number unsold:
\[
353 + 399 + 48 = 800
\]
### Summary of Answers:
- The number of purple sweet potato tarts: \( P \)
- The cost of the buffet for a child: NT\$[/tex]168
- The cost of the buffet for an elderly person: NT\[tex]$256
- The cost of the buffet for an adult: NT\$[/tex]399
- The total number of butter cookies: 800
Thus, the quantities are as follows:
1. The number of purple sweet potato tarts is [tex]\( P \)[/tex].
2. The buffet charge per child is NT\[tex]$168.
3. The buffet charge per elderly person is NT\$[/tex]256.
4. The buffet charge per adult is NT\$399.
5. The bakery has a total of 800 butter cookies.
