Question

Trina has two brothers. one brother is 7 years older than trina and the other brother is 7 years younger than trina. the product of her brothers age is 95.

a. if x represents trinas age, write an equation to describe the product of her brothers ages.
b. solve the equation for x how old is trina.

Answer 1

b and c are brothers
b=7+x
c=x-7

bc=95
a.
(x+7)(x-7)=95

b.
x^2-49=95
add 49 to both sides
x^2=144
sqrt both sides
x=12
tina=12

Answer 2

(a)
`(x-7)(x+7)=95`

(b) Trina is 12 years old.

Explanation:

(a)

Let x represents trinas age.

It is given that trina has two brothers. one brother is 7 years older than trina and the other brother is 7 years younger than trina.

Age of elder brother = x+7 years

Age of youger brother = x-7 years

Product of her brothers age =
`(x-7)(x+7)`

It is given that the product of her brothers age is 95.

`(x-7)(x+7)=95`

(b)

We need to solve the equation

`(x-7)(x+7)=95`

`x^2-7^2=95`
`[\because a^2-b^2=(a-b)(a+b)]`

`x^2-49=95`

Add 49 on both sides.

`x^2=95+49`

`x^2=144`

Taking square root both sides.

`x=\pm √(144)`

`x=\pm 12`

The values of x are -12 and 12. But age of a person can not be negative.

Therefore value of x is 12. It means trina is 12 years old.