Question

select the correct answer from each drop-down menu.

claires mother is 4 years more than twice claires age. the sum of their ages is 58 years.

claires age is choose an answer years, and her mothers age is choose an answer years.

Explanation:

Define variables for ages

Let \(c\) represent Claire's age in years.
Let \(m\) represent her mother's age in years.

Formulate the system of equations

Using Equation Formulation, we translate the word problem into mathematical statements:

1. "Claire's mother is 4 years more than twice Claire's age" translates to:

$$m = 2c + 4$$

1. "The sum of their ages is 58 years" translates to:

$$c + m = 58$$

Solve the system by substitution

Using Systems of Linear Equations, we substitute the expression for \(m\) from the first equation into the second equation:

$$c + (2c + 4) = 58$$

Solve for Claire's age

Using Linear Equations, we simplify and solve for \(c\):

$$3c + 4 = 58$$

$$3c = 54$$

$$c = 18$$

Calculate the mother's age

Substitute \(c = 18\) back into the expression for \(m\):

$$m = 2(18) + 4$$

$$m = 36 + 4$$

$$m = 40$$

Answer:

Claire's age is <blank>18</blank> years, and her mother's age is <blank>40</blank> years.