Question

kelly is 7 more than twice the age of her cousin molly. kelly is 15 years old.

if \\(x\\) is mollys age, which equation can represent the relationship between the two cousins ages?

how old is molly, to the nearest year?

select all that apply.

a \\(7x + 2 = 15\\)
b \\(7 + 2x = 15\\)
c 4 years old
d 2 years old
e 11 years old

Explanation:

Translate the word problem into an algebraic equation

We are given that \(x\) represents Molly's age.
"Twice the age of Molly" is represented as \(2x\).
"7 more than twice the age of Molly" is represented as \(2x + 7\) or \(7 + 2x\).
Since Kelly is 15 years old, we set this expression equal to 15:

$$7 + 2x = 15$$

This matches option (B).

Solve the equation for Molly's age

Using Word Problems modeling, we solve the linear equation for \(x\):

$$7 + 2x = 15$$

Subtract 7 from both sides:

$$2x = 8$$

Divide both sides by 2:

$$x = 4$$

Thus, Molly is 4 years old, which matches option (C).

Answer:

• (A) \(7x + 2 = 15\)
• (B) \(7 + 2x = 15\) (Correct answer)
• (C) 4 years old (Correct answer)
• (D) 2 years old
• (E) 11 years old