There were some mangosteens at a stall. In the morning, ¹₅ of mangosteens were sold. In the afternoon, another 31 mangosteens were sold. The total number of mangosteens sold was 5 less than ⁵₇ of the number of mangosteens the stall had at first.

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

	Comparison 1	Comparison 2
Before	5x7 =  35 u	7x5 =  35 u
Change 1	- 1x7 = - 7 u
After 1	4x7 =  28 u
Change 2	- 31
After 2	28 u - 31	5x5 - 5 = 25 u - 5

(a)
The number of mangosteens at first is repeated in both comparisons. Make the number of mangosteens at first.  LCM of 5 and 7 is 35.

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

28 u - 31 = 25 u - 5
28 u - 25 u = 31 - 5
18 u = 36

1 u = 36 ÷ 18 = 2

Number of mangosteens at first
= 35 u
= 35 x 2
= 70

(b)
Number of mangosteens that remained unsold
= 10 u + 5
= 10 x 2 + 5
= 25

Fraction of mangosteens that remained unsold
= ²⁵₇₀
= ⁵₁₄

Answer(s): (a) 70; (b) ⁵₁₄