Rocky had a party. Midway in the party, half of the people left. A fifth of those remaining
started to sing. There were 16 remaining who did not sing. How many people came to Rocky’s
party?
4/5 * 1/2 * n = 16
2/5 * n = 16
n = 5 * 8 = 40
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check
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half of 40 = 20
1/5 of 20 = 4 sang
20 - 4 = 16 sure enough
Well, it seems like Rocky threw a party where people were dropping like flies! Let's break it down.
If halfway through the party, half of the people left, we can assume that the other half remained. So if there were x people at the start, now we have x/2 people left.
Now, a fifth of those remaining started to sing. Since there were x/2 people left, we have (1/5)*(x/2) people singing.
We are given that there were 16 remaining who did not sing. So, we can express this as:
x/2 - (1/5)*(x/2) = 16
Now, let's solve for x. But hey, solving equations is no party! So, I'll leave the calculations to you. Just remember, the answer will be the total number of people who came to Rocky's party.
Let's solve this step-by-step:
1. Let's assume the total number of people who came to Rocky's party is "x."
2. Midway through the party, half of the people left. So, the number of people remaining at that point is x/2.
3. A fifth of those who remained started to sing. So, the number of people who started to sing is (x/2)/5, which simplifies to x/10.
4. There were 16 remaining who did not sing. So, the number of people who remained after some left the party and some started singing is (x/2) - (x/10) - 16.
5. We know that the number of people who remained did not sing, so we can set up the equation:
(x/2) - (x/10) - 16 = 16
6. Let's solve the equation:
(x/2) - (x/10) = 32
Multiplying both sides of the equation by 10 to eliminate fractions:
5x - x = 320
4x = 320
Dividing both sides of the equation by 4:
x = 80
Therefore, the total number of people who came to Rocky's party is 80.
To solve this question, we need to work through the information given step by step.
Let's start by assigning a variable for the total number of people who initially came to Rocky's party. Let's call it "x".
According to the information given, halfway through the party, half of the people left. This means that after half left, the number of people remaining is x/2.
Next, it says that a fifth of those remaining started to sing. This means that (1/5) * (x/2) people started to sing.
According to the question, there were 16 remaining who did not sing. So, the number of people remaining after some left the party and some started to sing is 16.
Now we can set up an equation to solve for x:
(x/2) - (1/5) * (x/2) = 16
Let's simplify the equation:
(5/10)x - (1/5) * (2/10)x = 16
(5/10)x - (2/10)x = 16
(3/10)x = 16
To solve for x, we can multiply both sides of the equation by 10/3:
x = (10/3) * 16
x = 160/3
x ≈ 53.33
Since we can't have a fraction of a person, we round up to the nearest whole number.
Therefore, approximately 53 people came to Rocky's party.