There were some mangosteens at a mart. In the morning, ¹₃ of mangosteens were sold. In the afternoon, another 28 mangosteens were sold. The total number of mangosteens left was 7 less than ³₈ of the number of mangosteens the mart had at first.

1. How many mangosteens were there at first?
2. What fraction of the mangosteens in the mart 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	- 28
After 2	16 u - 28	3x3 - 7 = 9 u - 7

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

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

16 u - 28 = 9 u - 7
16 u - 9 u = 28 - 7
7 u = 21

1 u = 21 ÷ 7 = 3

Number of mangosteens at first
= 24 u
= 24 x 3
= 72

(b)
Number of mangosteens that remained unsold
= 16 u - 28
= 16 x 3 - 28
= 48 - 28
= 20

Fraction of mangosteens that remained unsold
= ²⁰₇₂
= ⁵₁₈

Answer(s): (a) 72; (b) ⁵₁₈