Question

Directions: The following table shows the percentage population of six states (A to F) that lives below the poverty line, along with the male to female ratio among the population below the poverty line and above the poverty line, for each state.

State	% Population below poverty line	Below Poverty line M:F	Above Poverty line M:F
A	16	2:3	3:4
B	10	4:3	5:2
C	14	3:4	2:3
D	20	5:2	4:3
E	25	4:1	2:1
F	20	2:3	4:1

If the total population of state A is 5000, then what is the number of females above the poverty line in state A?

• A. 2000
• B. 2400
• C. 2600
• D. data inadequate

Hint:

First find 84% of 5000 for the population above poverty line, then split it using the 3:4 male to female ratio.

Answer 1

The Correct Option is B

Let's solve the problem step-by-step to find the number of females above the poverty line in State A.

1. Determine the population below the poverty line in State A:  
   \(16\%\) of the population lives below the poverty line. 
   Total population of State A = 5000 
   Population below poverty line = \(\frac{16}{100} \times 5000 = 800\)
2. Using the male to female ratio below the poverty line: 
   M:F = 2:3 
   Total parts = 2 + 3 = 5 
   Number of females = \(\frac{3}{5} \times 800 = 480\)
3. Calculate the population above the poverty line in State A: 
   Population above poverty line = Total population - Population below poverty line 
   Population above poverty line = 5000 - 800 = 4200
4. Using the male to female ratio above the poverty line: 
   M:F = 3:4 
   Total parts = 3 + 4 = 7 
   Number of females = \(\frac{4}{7} \times 4200 = 2400\)

Thus, the number of females above the poverty line in state A is 2400.

Answer 2

Step 1: Find the population above the poverty line in state A.
State A has 16% of its people below the poverty line, so \(100 - 16 = 84\%\) are above the poverty line. Total population of A is 5000, so people above the poverty line \( = 0.84 \times 5000 = 4200\).

Step 2: Use the male to female ratio for the above poverty line group.
From the table, the M:F ratio above the poverty line in A is \(3:4\). Add the parts: \(3 + 4 = 7\). So females make up \( \frac{4}{7} \) of that group.

Step 3: Calculate the number of females.
Females above the poverty line \( = \frac{4}{7} \times 4200 = 2400\). Check: males would be \( \frac{3}{7} \times 4200 = 1800\), and \(1800 + 2400 = 4200\), which matches the total above poverty line, so the split is correct.

Final Answer:
The number of females above the poverty line in state A is 2400. \[ \boxed{2400} \]