Cynthia's age is 2 years more than twice Bob's age. If the product of their ages is 60, how old is Cynthia?
To determine Cynthia's age, we need to set up equations based on the information given in the problem.
Let's assume Bob's age is x. According to the problem, Cynthia's age is 2 years more than twice Bob's age, which means Cynthia's age can be expressed as 2x + 2.
Now, we know that the product of their ages is 60. So, we can set up the equation:
x * (2x + 2) = 60
To solve this equation, we can simplify it:
2x^2 + 2x = 60
Rearranging the equation to bring all terms to one side gives us:
2x^2 + 2x - 60 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, factoring is a simpler method. We can factor out a common factor of 2:
2(x^2 + x - 30) = 0
Now factor the quadratic inside the parenthesis:
2(x - 5)(x + 6) = 0
From this, we get two possible values for x:
x - 5 = 0 or x + 6 = 0
Solving each equation gives us:
x = 5 or x = -6
Since age can only be positive, we discard the negative value. Therefore, Bob's age is 5.
Now, we can find Cynthia's age by substituting Bob's age into the expression we derived earlier:
Cynthia's age = 2x + 2 = 2 * 5 + 2 = 10 + 2 = 12
Therefore, Cynthia is 12 years old.
2B+2=C
BC=60 or C=60/B
2B+2=60/B
solve for B. Looks like a quadratic equation
B^2+ B-30=0 ...
(B+6)(B-5)=0
solutions, B=5, C=12