At the party,half the guests had left by 10pm. half the remaining guests left about 11pm.the last 6 stayed until midnight how many guests were at the party
1/2x + 1/4x + 6 = x
6 = 1/4x
6/(1/4) = x
24 = x
To find out how many guests were at the party, we can break down the information given step by step.
1. At 10 pm, half the guests had left. Let's call the initial number of guests "G". So, G/2 guests remained at 10 pm.
2. At 11 pm, half of the remaining guests left. From step 1, we know that G/2 guests remained at 10 pm. So, (G/2)/2 = G/4 guests remained at 11 pm.
3. Finally, at midnight, the last 6 guests stayed. So, the number of guests that remained at midnight is 6.
Now, we need to find the value of G, the initial number of guests. To do this, we can work backward from the last step to the first step.
1. At midnight, 6 guests remained.
2. At 11 pm, G/4 guests remained.
3. At 10 pm, G/2 guests remained.
Since we know that 6 guests remained at midnight, we can substitute this value into the equation for step 1:
6 = G/4
To solve for G, we can multiply both sides of the equation by 4:
6 * 4 = G
24 = G
Therefore, the initial number of guests at the party was 24.