Miss Goh sold 1/3 of her oranges on Saturday and 1/5 of the remainder on Sunday. She had 30 oranges left to sell on Monday. How many oranges did she have at first?

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Solution

Dear student,
$L e t t h e t o t a l n o . o f o r a n g e s M i s s G o h h a s b e' x' N o . o f o r a n g e s s o l d o n s a t u r d a y = \frac{1}{3} \times x = \frac{x}{3} R e m a i n i n g o r a n g e s = x - \frac{x}{3} = \frac{2 x}{3} N o . o f o r a n g e s s o l d o n s u n d a y = \frac{1}{5} \times \frac{2 x}{3} = \frac{2 x}{15} R e m a i n i n g o r a n g e s = \frac{2 x}{3} - \frac{2 x}{15} = \frac{10 x - 2 x}{15} = \frac{8 x}{15} N o w r e m a i n i n g n o . o f o r a n g e s = N o . o f o r a n g e s l e f t t o s e l l o n M o n d a y \Rightarrow \frac{8 x}{15} = 30 \Rightarrow x = \frac{30 \times 15}{8} \Rightarrow x = \frac{15 \times 15}{4} \Rightarrow x = \frac{225}{4} \Rightarrow x = 56.25 ≃ 56 o r a n g e s - - [a s n o . o f o r a n g e s c a n' t b e i n d e c i m a l]$
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