150k views
0 votes
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.

User Boisvert
by
7.9k points

2 Answers

3 votes
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
User Khaliah
by
8.2k points
7 votes

Answer:

(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.

User Cyberdelia
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories