Question

4. A ghost wants to distribute his x number of candies equally among his 7 friends. He realizes that he will have 2 candies left if he does so. If he had 5 more candies, he could distribute them equally. How many candies does he have?​

Answer 1

The ghost has 9 candies

Explanation:

Let's redefine "n" as the total number of groups of 7 candies that the ghost has, regardless of any remainder. We'll also introduce a new variable "k" to represent the number of additional candies beyond that. Then, the number of candies the ghost has can be expressed as:

x = 7n + 2

And the number of candies the ghost would have after receiving 5 more can be expressed as:

x + 5 = 7(n + 1) + k

(where "n + 1" represents the total number of groups of 7 candies, including the extra candies from the 5 additional ones).

To simplify this equation, we can substitute the first equation into the second:

7n + 2 + 5 = 7(n + 1) + k

Simplifying:

7n + 7 = 7(n + 1) + k

Expand:

7n + 7 = 7n + 7 + k

Subtract 7n and 7 from both sides:

k = 0

So, if the ghost had 5 more candies, he would have a total of 7(n+1) candies, with no remainder beyond groups of 7. Plugging this back into the first equation, we can solve for "n":

x + 5 = 7(n+1)

7n + 7 = 7(n+1)

Simplify:

n = 1

So, the ghost has:

x = 7n + 2 = 7(1) + 2 = 9

Therefore, the ghost has 9 candies.

Nice