Question

Victor is y years old.

His brother Fred is four years old than Victor.
The product of their ages is 780.
(a) Set up an equation to represent this information.
(b) Solve your equation from (a) to find Victors age

Answer 1

(a) y² + 4y - 780 = 0

(b) 26 years old

Explanation:

Equations:

f = y + 4 Eq. 1

f * y = 780 Eq. 2

Fred is f years old

Replacing Eq, 1 in Eq. 2

(y+4)*y = 780

y*y + 4*y - 780 = 0

y² + 4y - 780 = 0

(a) The equation that represents this information is:

y² + 4y - 780 = 0

Solve:

y = {-4±√((4²)-(4*1*780))} / (2*1)

y = {-4±√(16+3120} / 2

y = {-4±√3136} / 2

y = {-4±56} / 2

It refers to the age of some people, so, i will only take the positive data.

y = {-4+56}/2

y = 52/2

y = 26

From Eq. 1

f = y+4

f = 26 + 4

f = 30

Check:

from Eq. 2

f * y = 780

26*30 = 780

(b)

Victor´s age:

26 years old.

Fred´s age:

30 yeras old

Answer 2

Victor= 26 years old, Fred is 30

Explanation:

Fred = y + 4

Product = 780

y(y+4) = 780

y^2 + 4y = 780

y^2 + 4y - 780 = 0

y^2 + 30y - 26y - 780 = 0

y(y + 30) - 26(y + 30) = 0

(y - 26)(y + 30) = 0

Victor= 26 years old, Fred is 30