There were some persimmons at a market. In the morning, ¹₃ of persimmons were sold. In the afternoon, another 32 persimmons were sold. The total number of persimmons left was 4 less than ³₈ of the number of persimmons the market had at first.

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

	Comparison 1	Comparison 2
Before	3x8 =  24 u	8x3 =  24 u
Change 1	- 1x8 = - 8 u
After 1	2x8 =  16 u
Change 2	- 32
After 2	16 u - 32	3x3 - 4 = 9 u - 4

(a)
The number of persimmons at first is repeated in both comparisons. Make the number of persimmons at first.  LCM of 3 and 8 is 24.

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

16 u - 32 = 9 u - 4
16 u - 9 u = 32 - 4
7 u = 28

1 u = 28 ÷ 7 = 4

Number of persimmons at first
= 24 u
= 24 x 4
= 96

(b)
Number of persimmons that remained unsold
= 16 u - 32
= 16 x 4 - 32
= 64 - 32
= 32

Fraction of persimmons that remained unsold
= ³²₉₆
= ¹₃

Answer(s): (a) 96; (b) ¹₃