QuestionSuppose the members of population A, consisting of Al, Bob, Curt, Doris, and Ellie, receive annual incomes of , , , , and , respectively. What percentage of total income is received by the richest quintile?
A 25
B 50
C 5
D 20
Studdy Solution
STEP 1
What is this asking?
What part of all the money earned by these five people goes to the richest person?
Watch out!
Don't forget that a quintile represents one-fifth of the population, which in this case is just one person.
Also, remember to express the answer as a percentage!
STEP 2
1. Calculate total income
2. Calculate richest person's income share
3. Express as a percentage
STEP 3
Alright, let's **add up** all the incomes!
We're doing this to find the *total* income of the whole group.
It's like putting all the money in one big pile so we can see how much there is in total.
STEP 4
\(\$5000\) + \(\$2500\) + \(\$1250\) + \(\$750\) + \(\$500\) = \(\$10000\) So the **total income** earned by everyone is .
STEP 5
Now, let's see how much Al, the richest person, makes compared to the total.
We're doing this to find out *Al's share* of the total income.
STEP 6
Al earns , and the total income is , so Al's share is: \frac{\(\$5000\)}{\(\$10000\)}
STEP 7
Let's simplify this fraction by dividing both the numerator and denominator by .
We're dividing by because it's a common factor, and this makes the fraction easier to work with!
\frac{\(\$5000\)}{\(\$10000\)} = \frac{5 \cdot \(\$1000\)}{10 \cdot \(\$1000\)} = \frac{5}{10}
STEP 8
We can simplify further by dividing both the numerator and denominator by .
We're doing this to reduce the fraction to its simplest form!
Remember, dividing by is the same as multiplying by .
STEP 9
Finally, we need to express this fraction as a percentage.
We do this by multiplying the fraction by .
Multiplying by is the same as multiplying by , so we're not changing the value, just the way it's expressed!
STEP 10
The richest quintile (Al) receives \textbf{50%} of the total income.
So the answer is B.
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