Let's break down the solution step by step.
### Part 1: Number of Mixed Fruit Tarts and Purple Sweet Potato Tarts
We are given:
- The number of mixed fruit tarts is 147 less than that of purple sweet potato tarts.
Let's denote the number of purple sweet potato tarts as [tex]\( x \)[/tex].
Then, the number of mixed fruit tarts would be [tex]\( x - 147 \)[/tex].
In this case:
- The number of purple sweet potato tarts is [tex]\( x \)[/tex].
- The number of mixed fruit tarts is [tex]\( x - 147 \)[/tex].
So, the number of purple sweet potato tarts is simply [tex]\( x \)[/tex].
### Part 2: Cost of Buffet Per Adult
We are given:
- The buffet charges NT\[tex]$168 per child.
- This charge is NT\$[/tex]88 cheaper than that for the elderly.
Let's denote:
- Cost per child as [tex]\( C \)[/tex].
- Cost per elderly as [tex]\( E \)[/tex].
From the information provided:
[tex]\[ C = 168 \][/tex]
[tex]\[ E = C + 88 \][/tex]
[tex]\[ E = 168 + 88 = 256 \][/tex]
Further, we are given:
- The charge per adult is NT\[tex]$143 higher than the charge for the elderly.
Let's denote the cost per adult as \( A \).
From the information provided:
\[ A = E + 143 \]
\[ A = 256 + 143 = 399 \]
So, the buffet cost per adult is NT\$[/tex]399.
### Part 3: Number of Butter Cookies
We are given:
- The bakery sold 353 butter cookies in the morning.
- It sold 399 butter cookies in the afternoon.
- There are 48 unsold butter cookies left.
Let's denote:
- Number of cookies sold in the morning as [tex]\( M = 353 \)[/tex]
- Number of cookies sold in the afternoon as [tex]\( A = 399 \)[/tex]
- Number of unsold cookies as [tex]\( U = 48 \)[/tex]
To find the total number of cookies the bakery had, we add all these quantities together:
[tex]\[ \text{Total Butter Cookies} = M + A + U \][/tex]
[tex]\[ \text{Total Butter Cookies} = 353 + 399 + 48 = 800 \][/tex]
Thus, the total number of butter cookies the bakery has is 800.
### Summary
1. Number of Purple Sweet Potato Tarts: [tex]\( x \)[/tex] (where [tex]\( x \)[/tex] is the number of purple sweet potato tarts).
2. Number of Mixed Fruit Tarts: [tex]\( x - 147 \)[/tex].
3. Cost of Buffet per Adult: NT\$399.
4. Total Number of Butter Cookies: 800.
