Algebraic word problem

Question

Marc is 3 times as old as his brother, John. The sum of the squares of their ages two years ago was 178. If John is x years old, form an equation in x and show that it reduces to 5x²-8x-85=0.

Answer 1

m = Marc's age

x = John's age

 

Marc is 3 times as old as his brother, John:

m = 3x

 

The sum of the squares of their ages two years ago was 178:

(m-2)² + (x-2)² = 178

 

(3x-2)² + (x-2)² = 178

 

9x² -12x + 4 + x² - 4x + 4 = 178

10x² -16x + 8 = 178

2(5x² - 8x + 4) = 178

5x² - 8x + 4 = 89

5x² - 8x - 85 = 0