Rondrick had a certain number of sweets. If he gives 3 sweets to each of his friends, he will have 7 sweets left. If he gives 5 sweets to each of his friends, he will need 9 more sweets. How many friends does he have?
To solve this problem, we can use algebraic equations. Let's assume that Rondrick has "x" number of sweets and "y" number of friends.
According to the problem, if he gives 3 sweets to each of his friends, he will have 7 sweets left. This can be represented as:
x - 3y = 7 ----(1)
Similarly, if he gives 5 sweets to each of his friends, he will need 9 more sweets. This can be represented as:
x - 5y = -9 ----(2)
Now we have two equations with two variables. We can solve for "x" and "y" using any method of our choice. Here, we will use the elimination method.
Multiplying equation (1) by 5 and equation (2) by 3, we get:
5x - 15y = 35 ----(3)
3x - 15y = -27 ----(4)
Subtracting equation (4) from equation (3), we get:
2x = 62
x = 31
Now substituting the value of x in equation (1), we get:
31 - 3y = 7
-3y = -24
y = 8
Therefore, Rodrick has 8 friends.
Answer: Rondrick has 8 friends.
Let's assume Rondrick has "x" sweets and "y" friends.
If Rondrick gives 3 sweets to each of his friends, he will have 7 sweets left. This can be represented as:
x - 3y = 7 ........(1)
Similarly, if Rondrick gives 5 sweets to each of his friends, he will need 9 more sweets. This can be represented as:
x - 5y = -9 ........(2)
To solve this system of equations, we can use the method of substitution.
From equation (1), we can rewrite it as:
x = 3y + 7
Substitute this value of x into equation (2):
3y + 7 - 5y = -9
Simplify:
-2y + 7 = -9
Subtract 7 from both sides:
-2y = -16
Divide both sides by -2:
y = 8
Therefore, Rondrick has 8 friends.
To solve this problem, let's break it down step by step.
Let's assume Rondrick has "x" number of sweets.
According to the first condition, if he gives 3 sweets to each friend, he will have 7 sweets left. This can be represented as:
x - (3 * friends) = 7
According to the second condition, if he gives 5 sweets to each friend, he will need 9 more sweets. This can be represented as:
x - (5 * friends) = -9
Now we have a system of two equations. We can solve this system to find the value of "friends".
Step 1: Solve the first equation for "x":
x - 3friends = 7
x = 7 + 3friends
Step 2: Substitute the value of "x" in the second equation:
7 + 3friends - (5 * friends) = -9
Simplifying the equation:
7 - 9 = 5friends - 3friends
-2 = 2friends
Step 3: Solve for "friends":
2friends = -2
friends = -2/2
friends = -1
Uh-oh, it seems we have a problem. The result is -1, which doesn't make sense in this context. It's not possible for Rondrick to have a negative number of friends.
There might be an error in the problem statement or the solution may not exist.
I would recommend double-checking the problem and ensuring all the information is accurate.