There were some peaches at a supermarket. In the morning, ¹₃ of peaches were sold. In the afternoon, another 27 peaches were sold. The total number of peaches left was 9 less than ⁴₇ of the number of peaches the supermarket had at first.

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

	Comparison 1	Comparison 2
Before	3x7 =  21 u	7x3 =  21 u
Change 1	- 1x7 = - 7 u
After 1	2x7 =  14 u
Change 2	- 27
After 2	14 u - 27	4x3 - 9 = 12 u - 9

(a)
The number of peaches at first is repeated in both comparisons. Make the number of peaches at first.  LCM of 3 and 7 is 21.

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

14 u - 27 = 12 u - 9
14 u - 12 u = 27 - 9
2 u = 18

1 u = 18 ÷ 2 = 9

Number of peaches at first
= 21 u
= 21 x 9
= 189

(b)
Number of peaches that remained unsold
= 14 u - 27
= 14 x 9 - 27
= 126 - 27
= 99

Fraction of peaches that remained unsold
= ⁹⁹₁₈₉
= ¹¹₂₁

Answer(s): (a) 189; (b) ¹¹₂₁