Victor is y years old. His brother Fred is four years older than Victor. The product of their ages is 780. a) Set up an equation. b) Find Victor's age.

Here is the solution to problem 21: 21) Victor is y years old. His brother Fred is four years older than Victor. The product of their ages is 780. a) Set up an equation to represent this information. Step 1: Define the ages in terms of y. Victor's age = y Fred's age = y+4 Step 2: Write the equation for the product of their ages. y(y+4) = 780 Step 3: Expand the equation. y^2 + 4y = 780 The equation is: y^2 + 4y = 780 b) Solve your equation from (a) to find Victor's age. Step 1: Rearrange the equation into a standard quadratic form. y^2 + 4y - 780 = 0 Step 2: Solve the quadratic equation using the quadratic formula y = -b ± sqrt(b^2 - 4ac)2a. Here, a=1, b=4, and c=-780. y = -4 ± sqrt(4^2 - 4(1)(-780))2(1) y = -4 ± sqrt(16 + 3120)2 y = -4 ± sqrt(3136)2 Step 3: Calculate the square root. sqrt(3136) = 56 Step 4: Substitute the value back into the formula and find the two possible solutions for y. y = (-4 ± 56)/(2) For the first solution: y_1 = (-4 + 56)/(2) = (52)/(2) = 26 For the second solution: y_2 = (-4 - 56)/(2) = (-60)/(2) = -30 Step 5: Choose the valid solution. Since age cannot be negative, we discard y=-30. Therefore, Victor's age is 26 years. Victor's age is: 26 years old