Cynthia’s age is 5 years more than twice Bobs age. If the product of their ages is 102, how old is Cynthia?

Answer 1

C=5+2B

CB = 102

B= 102/C

C = 5+2(102/C) = 5 + 204/C

C^2 = 5C + 204

C^2 -5C = 204 complete the square, take half the C coefficient and square it. Add to both sides

C^2 -5C + 25/4 = 204 + 25/4

(C-5/2)^2 = 841/4

C=5/2 = (1/2)sqr841 = (1/2)29 = 14.5

C = 5/2 + 14.5 = 17 years old for Cynthia

B = 102/17 = 6 years old for Bob

17 = 2 times 6 plus 5