There were some persimmons at a supermarket. In the morning, ¹₄ of persimmons were sold. In the afternoon, another 36 persimmons were sold. The total number of persimmons left was 8 less than ⁵₁₂ of the number of persimmons the supermarket had at first.

1. How many persimmons were there at first?
2. What fraction of the persimmons in the supermarket remained unsold in the afternoon?

	Comparison 1	Comparison 2
Before	4x3 =  12 u	12x1 =  12 u
Change 1	- 1x3 = - 3 u
After 1	3x3 =  9 u
Change 2	- 36
After 2	9 u - 36	5x1 - 8 = 5 u - 8

(a)
The number of persimmons at first is repeated in both comparisons. Make the number of persimmons at first.  LCM of 4 and 12 is 12.

The number of persimmons in the end is the same in both comparisons.

9 u - 36 = 5 u - 8
9 u - 5 u = 36 - 8
4 u = 28

1 u = 28 ÷ 4 = 7

Number of persimmons at first
= 12 u
= 12 x 7
= 84

(b)
Number of persimmons that remained unsold
= 9 u - 36
= 9 x 7 - 36
= 63 - 36
= 27

Fraction of persimmons that remained unsold
= ²⁷₈₄
= ⁹₂₈

Answer(s): (a) 84; (b) ⁹₂₈