Mathematics 2019 JAMB Past Questions - Question 28: The ages of Tosan and Isa differ by 6 and the product of their ages is 87. Write their ages in the form of (x,y) where x>y.

Correct Answer

C

Explanation

To solve this problem, we can use a system of equations. Let's denote Tosan's age as \( x \) and Isa's age as \( y \). We are given two pieces of information:1. The ages differ by 6: \( x - y = 6 \)2. The product of their ages is 87: \( xy = 87 \)We can solve this system of equations to find the values of \( x \) and \( y \). One way to do this is to solve for one variable in terms of the other using the first equation, and then substitute this expression into the second equation.From the first equation, we can express \( x \) in terms of \( y \) as \( x = y + 6 \). Substituting this into the second equation gives us:\[ (y + 6)y = 87 \]\[ y^2 + 6y - 87 = 0 \]We can solve this quadratic equation to find the values of \( y \). The solutions are \( y = 6 \) and \( y = -12 \). Since we are looking for positive ages, the solution is \( y = 6 \). Substituting this back into the equation \( x = y + 6 \) gives us \( x = 12 \).So, the ages of Tosan and Isa are (12, 6). Therefore, the answer is A. (12, 6).