A boy purchased some chocolates from a shop for $ 120. In the next sho

Solution – Using Options

• A boy purchased some chocolates from a shop for $120.
• In the next shop he found that the price per piece of chocolate is $3 less than that charged at the previous shop.
• Because of the lower price in the next shop, he figured out that he could have purchased 2 more chocolates in the next shop, compared to what he bought originally.

• The number of chocolates he bought from the first shop

• 120/number of chocolates bought = price per chocolate
• Therefore, number of chocolates bought must be a factor of 120 (at this point, we can discard option A and option C)

• 120/(number of chocolates bought + 2) = price per chocolate – 3
• Therefore, (number of chocolates bought + 2) must also be a factor of 120 (at this point, we can discard option E)

• Price per chocolate in the first shop = \(\frac{120}{8} = 15\)
• Price per chocolate in the second shop = \(\frac{120}{(8 + 2)} = 12\)
• And, 15 – 12 = 3, which satisfies our given condition.

Solution – Using 1 Variable

• A boy purchased some chocolates from a shop for $120.
• In the next shop he found that the price per piece of chocolate is $3 less than that charged at the previous shop.
• Because of the lower price in the next shop, he figured out that he could have purchased 2 more chocolates in the next shop, compared to what he bought originally.

• The number of chocolates he bought from the first shop

• Price per chocolate in the first shop = \(\frac{120}{n}\)

• Price per chocolate in the second shop = \(\frac{120}{(n + 2)}\)

• \(\frac{120}{n} – \frac{120}{n+2} = 3\)
Simplifying, we get n = 8

Solution – Using 2 Variables

• A boy purchased some chocolates from a shop for $120.
• In the next shop he found that the price per piece of chocolate is $3 less than that charged at the previous shop.
• Because of the lower price in the next shop, he figured out that he could have purchased 2 more chocolates in the next shop, compared to what he bought originally.

• The number of chocolates he bought from the first shop

• Therefore, we can say n x p = 120 …… (1)

• Therefore, we can say that (n + 2) (p – 3) = 120 …… (2)