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Below are the quantities of three types of food in the delicious cake shop.

1. The number of mixed fruit tarts is 147 less than that of purple sweet potato tarts. How many purple sweet potato tarts are there?

2. The buffet charges NT[tex]$168 per child, which is NT$[/tex]88 cheaper than the elderly. The charge per adult is NT$143 higher than the elderly. How much does the buffet cost per adult?

3. The bakery sold 353 butter cookies in the morning and 399 butter cookies in the afternoon, leaving 48 unsold butter cookies. How many butter cookies does the bakery have?

Sagot :

GinnyAnswer
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.
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