sweets are shared equally among 20 children at a party. if there were 1 more sweet and 1 more child, each child would get 1 sweet less. how sweets were shared at the party?
thats how the question ends.
To solve this problem, let's break it down into steps:
Step 1: Define the variables:
- Let's assume that initially, X sweets were shared among 20 children. Therefore, each child would receive X/20 sweets.
Step 2: Set up the equation:
- According to the problem, if there were 1 more sweet and 1 more child, each child would receive 1 sweet less.
- So, if we add 1 sweet and 1 child to the original scenario, the new sweets shared among the children would be: (X+1) sweets shared among (20+1) children.
- And each child would receive (X+1)/(20+1) sweets.
Step 3: Write the equation:
- Based on the given information, we can set up the equation as follows:
(X+1)/(20+1) = X/20 - 1
Step 4: Solve the equation:
- Now, let's solve the equation for X, which represents the number of sweets initially shared.
Multiply both sides of the equation by (20+1) and 20 to eliminate the denominators:
(20+1)(X+1) = X(20+1) - 20
21X + 21 = 21X + X - 20
The X term cancels out on both sides, which leaves us with:
21 = -20
Step 5: Analyze the result:
- We arrive at an incorrect equation (21 = -20), which means there is no solution to this problem.
Therefore, based on the information given, there is no way to determine how the sweets were shared at the party as the question seems to have an error.
You might use algebra to solve this. (Hooray! Everyone loves algebra!)
Let's create some variables:
s = number of sweets
n = number of sweets each child gets.
So we have sweets shared equally among 20 children:
s / 20 = n
Also, 1 more sweet and 1 more child means 1 less sweet for each child:
(s + 1) / (20 + 1) = (n - 1)
Does that make sense? If so, can you take it from here?