To solve the problem regarding the quantities of tarts in the delicious cake shop, let's define our variables and work through the solution step-by-step.
1. Define Variables:
- Let [tex]\( x \)[/tex] represent the number of purple sweet potato tarts.
- Let [tex]\( y \)[/tex] represent the number of mixed fruit tarts.
2. Formulate the Relationship:
According to the problem, the number of mixed fruit tarts is 147 less than the number of purple sweet potato tarts. This can be written as:
[tex]\[
y = x - 147
\][/tex]
3. Understand the Problem:
The problem asks for the number of purple sweet potato tarts, which we have represented as [tex]\( x \)[/tex].
4. Express the Quantities:
- The number of purple sweet potato tarts is [tex]\( x \)[/tex].
- The number of mixed fruit tarts is [tex]\( x - 147 \)[/tex].
Since these expressions for the quantities of tarts are a function of [tex]\( x \)[/tex], we have:
- Mixed fruit tarts: [tex]\( y = x - 147 \)[/tex]
- Purple sweet potato tarts: [tex]\( x \)[/tex]
Thus, the number of purple sweet potato tarts is [tex]\( x \)[/tex], and the number of mixed fruit tarts is [tex]\( x - 147 \)[/tex].
Therefore, depending on the specific value of [tex]\( x \)[/tex], which isn't provided in the problem statement, you can determine the exact quantities. If you were given a specific total number of tarts or additional constraints, you could solve for [tex]\( x \)[/tex].
In conclusion:
If you know the value of [tex]\( x \)[/tex] (number of purple sweet potato tarts), the number of mixed fruit tarts would be [tex]\( x - 147 \)[/tex]. However, without additional information, [tex]\( x \)[/tex] remains the variable representing the number of purple sweet potato tarts.
