There were some grapefruits at a mart. In the morning, ¹₆ of grapefruits were sold. In the afternoon, another 28 grapefruits were sold. The total number of grapefruits sold was 2 less than ⁵₁₂ of the number of grapefruits the mart had at first.

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

	Comparison 1	Comparison 2
Before	6x2 =  12 u	12x1 =  12 u
Change 1	- 1x2 = - 2 u
After 1	5x2 =  10 u
Change 2	- 28
After 2	10 u - 28	5x1 - 2 = 5 u - 2

(a)
The number of grapefruits at first is repeated in both comparisons. Make the number of grapefruits at first.  LCM of 6 and 12 is 12.

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

10 u - 28 = 5 u - 2
10 u - 5 u = 28 - 2
3 u = 30

1 u = 30 ÷ 3 = 10

Number of grapefruits at first
= 12 u
= 12 x 10
= 120

(b)
Number of grapefruits that remained unsold
= 7 u + 2
= 7 x 10 + 2
= 72

Fraction of grapefruits that remained unsold
= ⁷²₁₂₀
= ³₅

Answer(s): (a) 120; (b) ³₅