Got this problem in Algebra 2 and i need help like fast!!!??

Question

The ages of three sisters are consecutive even integers. The product of the ages of the oldest and youngest sisters is 20 more than twice the middle sister’s age.

a. Write an equation that can be solved to find the age, x, of the youngest sister.

b. Solve the equation you wrote in part a. to find the age of the youngest sister. Show your work or explain how you know.

c. What will the sum of the three sisters’ ages be in 7 years?

Answer 1

As the problem states, let x = the current age of the youngest sister. Since the ages of the sisters are consecutive even integers, the age of the middle sister is x+2 and the age of the oldest sister is x+4. The problem states that the product of the ages of the youngest and oldest sister, x*(x+4) is 20 more than twice the middle sister's age. The equation is therefore

x*(x+4) = 2(x+2) +20

Simplify to get x^2 +4x = 2x + 24

Rearrange to get

x^2 + 2x -24 = 0

Factor to get (x+6)*(x-4) = 0. Therefore, either x+6 = 0, in which case x = -6, or

x-4 =0, in which case x=4. Since x is an age, reject the negative value. Therefore, the age of the youngest sister is 4, and her other sisters are 6 and 8 years old, respectively.

In seven years the sisters will be 11, 13 and 15 years old. The sum of these ages is 39.

Answer 2

3 consecutive even integers means the ages are:

Youngest: X

Middle: X+2

Oldest: X+4

Product of oldest and youngest

(x)(x+4)

20 more than twice the middle sister’s age

2(x+2) + 20

So

(x)(x+4) = 2(x+2) + 20

Simplify each side

x² + 4x = 2x + 4 + 20

Combine like terms (subtract 2x on both sides and add 20 and 4)

x² + 2x = 24

a) x² + 2x - 24 = 0

b) solve:

(x + 6)(x -4) = 0

x + 6 = 0

X = -6

x -4 = 0

X = 4

Since it's an age and age can't be negative, then the only answer is that the youngest is 4 years old.

C) currently they are 4, 6 and 8. So in 7 years they will be 11, 13, 15. Sum is 39.