N_a = Current fatal accident rate for drinking men per billion miles driven = 11 = A + A² + AB + AC + AD, where A = their expected accident rate independent of other drivers.

N_b = Current accident rate of drinking women = 6 = B + B² + AB + BC + BD, where B = expected rate independent of other drivers.

N_c = Current accident rate of non-drinking men = 47 = C + C² + AC + BC + CD

N_d = Current accident rate of non-drinking women = 75 = D + D² + AD + BD + CD

A = (75 - D - D² - BD - CD)/D

B = (47 - C - C² - AC - CD)/C

C = (6 - B - B² - AB - BD)/B

D = (11 - A - A² - AB - AC)/A

D² = (121 - 22A - 22AC - 22AB - 21A² + 2A²C + 2A²B + 2A²BC + A²C² + A²B² +2A³ +2A³B +2A³C)/A²        

A =  (75 - (11 - A - A² - AB - AC)/A - (121 - 22A - 22AC - 22AB - 21A² + 2A²C + 2A²B + 2A²BC + A²C² + A²B² +2A³ +2A³B +2A³C)/A² - B(11 - A - A² - AB - AC)/A - C(11 - A - A² - AB - AC)/A)/(11 - A - A² - AB - AC)/A

A = 75A - (11 - A - A² - AB - AC - (121 - 22A - 22AC - 22AB - 21A² + 2A²C + 2A²B + 2A²BC + A²C² + A²B² +2A³ +2A³B +2A³C)/A - 11B + AB ⁺ A²B + AB² + ABC - 11C + AC + A²C + ABC - AC²)/(11 - A - A² - AB - AC)

A² = 75A² - 11A + A²  + A³ + A²B + A²C + 121 - 22A - 22AC - 22AB - 21A² + 2A²C + 2A²B + 2A²BC + A²C² + A²B² +2A³ +2A³B +2A³C - 11AB + A²B ⁺ A³B + A²B² + A²BC - 11AC + A²C + A³C + A²BC - A²C²)/(11A - A² - A³ - A²B - A²C)

11A³ - A⁴ - A⁵ - A⁴B - A⁴C = 75A² - 11A + A²  + A³ + A²B + A²C + 121 - 22A - 22AC - 22AB - 21A² + 2A²C + 2A²B + 2A²BC + A²C² + A²B² +2A³ +2A³B +2A³C - 11AB + A²B ⁺ A³B + A²B² + A²BC - 11AC + A²C + A³C + A²BC - A²C²

B = (47 - C - C² - (75C - CD -CD² - BCD - C²D)/D - 75 - D - D² - BD - CD)/ (75 - D - D² - BD - CD)/D

B = (47D - CD - C²D - 75C - CD -CD² - BCD - C²D - 75D - D² - D³ - BD² - CD²)/ (75 - D - D² - BD - CD)

75B - BD - BD² - B²D - BCD = 47D - CD - C²D - 75C - CD -CD² - BCD - C²D - 75D - D² - D³ - BD² - CD²

75B - BD - 0BD² - B²D - 0BCD +28D +2CD +2C²D -75C +0CD² +D² +D³ = 0

75B - BD - B²D +28D +2CD +2C²D -75C +D² +D³ = 0

A² = (5625 - 150D - 149D² - 150DB +2D³ -150DC +2D²B + D⁴ +2D³B + 2D²C + 2D³C + D²B² +2D²BC +D²C²)/D²  

11 = (75 - D - D² - BD - CD)/D + (5625 - 150D - 149D² - 150DB +2D³ -150DC +2D²B + D⁴ +2D³B + 2D²C + 2D³C + D²B² +2D²BC +D²C²)/D²  +  (75B - BD - BD² - B²D - BCD)/D +  (75C - CD - CD² - CBD - C²D)/D  + 75 - D - D² - BD - CD

11D² = 75D - D² - D³ - BD² - CD² + 5625 - 150D - 149D² - 150DB +2D³ -150DC +2D²B + D⁴ +2D³B + 2D²C + 2D³C + D²B² +2D²BC +D²C² + 75BD - BD² - BD³ - B²D² - BCD² + 75CD - CD² - CD³ - CBD² - C²D² + 75D² - D³ - D⁴ - BD³ - CD³  

5625 -75D - 86D² + 0D³ - 0BD² -75BD -75CD +0D⁴ + 0D³B +  0CD² +0D³C +0D²B² + 0D²BC +0D²C² - 0CD³ = 0                     

5625 -75D - 86D² -75BD -75CD = 0

75BD = 5625 -75CD -75D - 86D² 

B = (5625 -75CD -75D - 86D²)/75D 

A = (75 - D - D² - BD - CD)/D

A = (75 - D - D² - ((5625 -75CD -75D - 86D²)/75) - CD)/D

A = (5625 - 75D - 75D² - 5625 +75CD +75D + 86D² - 75CD)/75D

A = 11D²/75D = 11D/75

47 = C + C² + AC + AB + AD

47 = C + C² + 11CD/75 + 11BC/75 + 11D²/75

47 = (C + C² + 11CD/75 + (61875C - 825C²D -825CD -946CD²)/5625D + 11D²)/75

3525 = C + C² + 11CD/75 + (61875C - 825C²D -825CD -946CD²)/5625D + 11D²

19,828,125 ⁼ 5625CD + 5625C²D + 825CD² + 61875C - 825C²D -825CD -946CD² + 61875D³

19,828,125 ⁼ 4800CD + 4800C²D - 121CD² + 61875C + 61875D³

A = (75 - D - D² - BD - CD)/D = 11D/75

(5625 -75D -75D² - 75BD - 75CD)/D = 11D

5625 -75D -75D² - 75BD - 75CD = 11D²

86D² + 75D + 75BD + 75CD - 5625 = 0

75BD = 5625 -75CD -75D - 86D²

86D² + 75D +  5625 -75CD -75D - 86D² + 75CD - 5625 = 0

75 = D + D² + AD + BD + CD

75 = D + D² + 11D²/75 + (5625 -75CD -75D - 86D²)/75 + CD

5625 = 75D + 75D² + 11D² + 5625 -75CD -75D - 86D² + 75CD

0 = 0D + 0D² + 0D + 0CD