please help me with this question

Question

John has an unknown number of sweets which he wants to distribute equally amongst himself and 4 of his friends. he and his friends receive 17 sweets with 2 odd sweets left.

Hint: take the unknown number of sweets as x

(a) design an equation whereby you can determine how many sweets John started with.
(b) use the equation to calculate how many sweets did John start with.

Answer 1

(a) Let x represent the unknown number of sweets that John started with.

When John distributes the sweets equally among himself and his 4 friends, each person receives (x/5) sweets.

But there are 2 odd sweets left, which means that the total number of sweets must be 2 more than a multiple of 5.

Therefore, the equation can be written as:
x ≡ 2 (mod 5)

(b) To calculate how many sweets John started with, we need to find a value of x that satisfies the equation x ≡ 2 (mod 5).

From the given information, we know that John and his friends received 17 sweets:
(x/5) + (x/5) + (x/5) + (x/5) + (x/5) = 17
5x/5 = 17
5x = 85
x = 17

Therefore, John started with 17 sweets.