Question

Of the 34 students in a class there are 2 fewer students with blue eyes than there are with hazel eyes. also there are twice as many students with brown eyes. which of these is either the number of students with blue eyes the number of students with brown eyes or the number of students with hazel eyes. select all that apply.

A. 8
B. 10
C. 12
D. 16
E. 20
F. 34​

Answer 1

D

Explanation:

bl is blue eyes h = hazel eyes br = brown eyes

eq 1) bl + h + br = 34 sum of all the students

eq 2) bl + 2 = h blue eyes plus 2 equal hazel eyes

eq 3) br = 2( bl + h ) there are twice as many brown eyed student

as blue eyed and hazel eyed students

eq 1) bl + h + br = 34 substitute for h in eq 2) bl + 2 = h

bl + (bl + 2) + br = 34

eq 4) 2bl + 2 + br = 34 a new equation is created without h

eq 3) br = 2(bl + h) substitute in for h into eq 3) using eq 2)

br = 2bl + 2h remember eq 2 was be + 2 = h

br = 2bl + 2(bl + 2)

eq 5) br = 4bl + 4 another eq WITHOUT h

now solve eq 4) and eq 5) by subsitition

eq 5) br = 4bl + 4 sub bl into eq 4)

eq 4) 2bl + 2 + br = 34

2bl + 2 + (4bl + 4) = 34 ONE equation with ONE unknown

solve for bl

2bl + 4bl + 2 + 4 = 34

6bl + 6 = 34

6bl + 6 - 6 = 34 - 6

6bl = 28

3bl = 14

bl = 14/3 = 4 2/3 so who has the 2/3 eye???

none of these numbers match the solution options

need to check my answer for sure my math was correct

bl + h + br = 34 bl = 14/3

eq 2) bl + 2 = h 14/3 + 6/3 = h h = 20/3

eq 3) br = 2( bl + h )

br = 2(14/3 + 20/3)

br = 2(34/3)

br = 68/3

bl + h + br = 34

14/3 + 20/3 + 68/3 = 102/3 102/3 = 34 the numbers check

************ i suspect the equation was typed incorrectly ****************

if the total number of students were 36

blue eyes = 5

hazel eyes = 7

brown eyes = 2 times (5 +7) = 24

5 + 7 + 24 = 36

again none of these numbers match option

if the total number of students were 24

blue eyes = 3

hazel eyes = 5

brown eyes = 2 times (5 +7) = 16 D = 16

3 + 5 + 16 = 24