Question

A girl is 6 years younger than her brother. The
product of their ages is 135. Find their ages.​

Answer 1

Okay to do this you will need to set up a simple equation and give out variables.
Girls age = x-6
Brother's age= *
the you will take those 2 and add them and place them equil to 135 like so:

x-6+x=135
2x-6+6=135+6
2x=141
2x/2=141/2
x=70.5
The brothers age would be 70.5 then and the girl's would be 64.5

Answer 2

• Brother's age = 15
• Sister's age = 9

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Work Shown:

x = brother's age, which is some positive whole number

x-6 = sister's age, since she is 6 years younger than her brother

The product is the result of multiplication, so we multiply x and (x-6) to get 135

x*(x-6) = 135

x^2-6x = 135

x^2-6x-135 = 0

Use the quadratic formula to solve from here

We plug in a = 1, b = -6, c = -135

`x = (-b\pm√(b^2-4ac))/(2a)\\\\x = (-(-6)\pm√((-6)^2-4(1)(-135)))/(2(1))\\\\x = (6\pm√(576))/(2)\\\\x = (6\pm24)/(2)\\\\x = (6+24)/(2)\ \text{ or } \ x = (6-24)/(2)\\\\x = (30)/(2)\ \text{ or } \ x = (-18)/(2)\\\\x = 15\ \text{ or } \ x = -9\\\\`

x represents the brother's age, in years. So x must be positive.

Since x must be positive, this means we rule out x = -9

The value x = 15 is the only practical solution.

If x = 15, then x-6 = 15-6 = 9

The brother is 15 years old and the sister is 9 years old.

The product of their ages is 15*9 = 135, which confirms the answers.