Let's determine the number of purple sweet potato tarts using algebra. The problem states that the number of mixed fruit tarts is 147 less than the number of purple sweet potato tarts.
To find the number of purple sweet potato tarts, follow these steps:
1. Define the Variables:
- Let [tex]\( x \)[/tex] be the number of purple sweet potato tarts.
- Let [tex]\( y \)[/tex] be the number of mixed fruit tarts.
2. Set Up the Relationship:
- According to the problem, the number of mixed fruit tarts is 147 less than the number of purple sweet potato tarts. Therefore, we can write the equation:
[tex]\[
y = x - 147
\][/tex]
3. To find [tex]\( x \)[/tex]:
- Rearrange the equation to solve for [tex]\( x \)[/tex] if needed, but in this case, we note that the relationship [tex]\( y = x - 147 \)[/tex] gives a straightforward way to compute [tex]\( y \)[/tex] once [tex]\( x \)[/tex] is known.
- However, we are given that [tex]\( y \)[/tex] is explicitly defined as 147 less than the quantity of [tex]\( x \)[/tex], therefore we only know that the exact additional detail relies on knowing [tex]\( y \)[/tex] for complete validation.
Currently, without any more details on the specific [tex]\( y \)[/tex] or numerical values for the mixed fruit tarts directly, we state the direct interpreted quantity is being strictly referred where:
[tex]\[
x\text{ (purple sweet potato tarts)} \text{ and with } \ y\, (mixed tart) = x-147
\][/tex]
Hence, If [tex]\( y\)[/tex] value if required directly should be explicit given number to conclude [tex]\( x\)[/tex] substitution considering those provided criteria directly calculation $\left[y: \left(\measured simulated \quad facto were clearly specific \right):\text{} \text{number of purple sweet potato tarts}\ x\ ]}.
