Question

Casey asks a random sample of students at his school about their natural hair and eye colors. The results of his survey are shown in
the relative frequency table below.
Black
Brown
Hair
Red
Color
Blonde
Total
Brown
0.225
0.350
0,025
0.050
0.650
Eye Color
Blue Other
0.000 0.025
0.125 0.100
0.000 0.025
0.075 0.000
0.200 0.150
Total
0.250
0.575
0.050
0.15
1.000
In the sample, there are 4 more students with brown hair and blue eyes than blond hair and blue eyes.
How many total students have black hair?

Answer 1

Answer:   20

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Explanation:

x = total number of students surveyed

According to the table, 0.075 of the students (aka 7.5%) have blond hair and blue eyes. This means 0.075x is the number of blond hair blue eye people.

Also, 0.125x is the number of brown hair blue eye people for similar reasoning as the previous paragraph.

We're told that "There are 4 more students with brown hair and blue eyes than blond hair and blue eyes"

So,

(BrownHair_BlueEyes) = (BlondHair_BlueEyes) + 4

0.125x = (0.075x) + 4

0.125x-0.075x = 4

0.05x = 4

x = 4/0.05

x = 80

There are 80 students surveyed.

Of those eighty students,  0.075x = 0.075*80 = 6 have blond hair and blue eyes; while 0.125x = 0.125*80 = 10 have brown hair and blue eyes. Notice how this is four more than the blond person count with blue eyes. This confirms we have the correct sample size.

The last step is to calculate how many of the students have black hair based on the sample size we just found.

The table shows 25% = 0.250 of the students have black hair, so 0.25x = 0.25*80 = 20 students have black hair