There were some grapefruits at a shop. In the morning, ¹₅ of grapefruits were sold. In the afternoon, another 21 grapefruits were sold. The total number of grapefruits left was 6 less than ⁵₇ of the number of grapefruits the shop had at first.

1. How many grapefruits were there at first?
2. What fraction of the grapefruits in the shop 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	- 21
After 2	28 u - 21	5x5 - 6 = 25 u - 6

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

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

28 u - 21 = 25 u - 6
28 u - 25 u = 21 - 6
3 u = 15

1 u = 15 ÷ 3 = 5

Number of grapefruits at first
= 35 u
= 35 x 5
= 175

(b)
Number of grapefruits that remained unsold
= 28 u - 21
= 28 x 5 - 21
= 140 - 21
= 119

Fraction of grapefruits that remained unsold
= ¹¹⁹₁₇₅
= ¹⁷₂₅

Answer(s): (a) 175; (b) ¹⁷₂₅