When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be purchased for the original price. How many oranges can be purchased for 24 dollars at the original price?

Created: 3 months ago | Updated: 3 months ago

$L e t, o r i g i n a l \cos t p r i c e o f a n o r a n g e i s x d o l l a r .$

$A t 40 % d i s c o u n t, t h e p r i c e o f a n o r a n g e i s$

$= 60 % o f x = \frac{60 x}{100} = \frac{3 x}{5} D o l l a r$

$A c c o r d i n g t o t h e q u e s t i o n$

$\frac{12}{\frac{3 x}{5}} - \frac{12}{x} = 4 = 12 \times \frac{5}{3 x} - \frac{12}{x} = 4$

$= \frac{20}{x} - \frac{12}{x} = 4 = \frac{20 - 12}{x} = 4 = \frac{8}{x} = 4$

$∴ x = \frac{8}{4} = 2$

$∴ N u m b e r o f o r a n g e s t h a t c a n b e p u r c h a s e d b y 24 d o l l a r s = \frac{24}{2} = 12 (a n s w e r$ )

3 months ago

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Train X leaves New York at 10.00 AM and travels East at a constant speed of x miles per hour. If another Train Y leaves New York at 11.30AM and travels East along the same tracks at speed $\frac{4 x}{3}$ then at what time will Train Y catch Train X?

Created: 3 months ago | Updated: 3 months ago

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