Declarations
Let Brenda's age be B
Let Jason's age be J
Equations
[tex]\dfrac{B}{J}=\dfrac{4}{5}\\ \\ \dfrac{(B+8)}{(J+8)} = \dfrac{6}{7}[/tex]
Solution
Cross multiply both fractions
5B = 4J (1)
7(B + 8) = 6(J + 8) Remove the brackets on both sides.
7B + 56 = 6J + 48 Subtract 48 from both sides
7B + 56 - 48 = 6J
7B + 8 = 6J (2)
Use Equation (1) to solve for J
5B = 4J Divide by 4
5B/4 = J Pult this result in equation 2
7B + 8 = 6*( 5B/4)
7B + 8 = 30*B/4
7B + 8 = 7.5 B Subtract 7B from both sides.
8 = 7.5B - 7B
8 = 0.5 B Divide by 0.5
B = 8/0.5
B = 16 <<<< Answer
