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.
(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.
Sure, let's solve the problem step-by-step:
(a) To determine how many sweets John started with, we can create an equation based on the given information. We know that John wants to distribute the sweets equally among himself and 4 friends, so the total number of sweets must be divisible by 5 (John and his 4 friends).
Let's use the unknown number of sweets as "x". We can set up the equation as follows:
x % 5 = 2
The remainder (modulus) when you divide "x" by 5 should be equal to 2 because 2 sweets are left. This equation represents the fact that the total number of sweets, "x", when divided by 5 should have a remainder of 2.
(b) Now, let's solve the equation to find the value of "x" and determine how many sweets John started with.
We can use trial and error to find a number that satisfies the equation. Start by trying different values of "x" that give a remainder of 2 when divided by 5.
Let's try some values:
- If x = 2, then 2 % 5 = 2 (not divisible by 5)
- If x = 7, then 7 % 5 = 2 (divisible by 5)
So, John started with 7 sweets.
Therefore, John started with 7 sweets.
To solve this problem, we'll need to set up an equation based on the given information and solve for the unknown number of sweets John started with. Let's go step by step:
(a) Designing the equation:
1. Assume the unknown number of sweets John started with is x.
2. Since John wants to distribute them equally among himself and 4 friends, each person will receive x/5 sweets.
3. We are told that John and his friends receive 17 sweets in total, with 2 odd sweets left.
4. So, we can set up the equation: (x/5) * 5 + 2 = 17.
(b) Solving the equation:
1. Simplify the equation by multiplying x/5 with 5: x + 2 = 17.
2. Subtract 2 from both sides of the equation: x = 15.
Therefore, John started with 15 sweets.
To verify our answer, we can substitute 15 into the equation: (15/5) * 5 + 2 = 3 * 5 + 2 = 15 + 2 = 17. Thus, our answer is correct.