Asked by Ellie
please help me with this 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.
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.
Answers
Answered by
GPT 3.5
(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.
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.