Answer: There are 80 items he originally have.
Step-by-step explanation:
Since we have given that
Part of refreshments were granola = ![\dfrac{1}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B5%7D)
Part of refreshments were popcorns = ![\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D)
Remaining part would be
![1-(\dfrac{1}{5}+\dfrac{1}{2})\\\\=1-\dfrac{7}{10}\\\\=\dfrac{10-7}{10}\\\\=\dfrac{3}{10}](https://tex.z-dn.net/?f=1-%28%5Cdfrac%7B1%7D%7B5%7D%2B%5Cdfrac%7B1%7D%7B2%7D%29%5C%5C%5C%5C%3D1-%5Cdfrac%7B7%7D%7B10%7D%5C%5C%5C%5C%3D%5Cdfrac%7B10-7%7D%7B10%7D%5C%5C%5C%5C%3D%5Cdfrac%7B3%7D%7B10%7D)
Since rest were divided equally among apples, rice cakes, and yogurt.
Number of apples sold = 8
Let the total number of items be 'x'.
According to question, it becomes,
![\dfrac{3}{10}\times \dfrac{1}{3}x=8\\\\\dfrac{x}{10}=8\\\\x=80](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B10%7D%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7Dx%3D8%5C%5C%5C%5C%5Cdfrac%7Bx%7D%7B10%7D%3D8%5C%5C%5C%5Cx%3D80)
Hence, there are 80 items he originally have.