Question

Three siblings are comparing their ages. Jenna is the youngest. Her brother Carl is 6 years older than her. Her sister Eve is twice her age. The sum of their ages is 42. Let j represent Jenna's age. Write expressions for both Carl's age and Eve's age in terms of j, and write and solve an equation for j. State the ages of all three siblings. a) Carl's age: j + 6, Eve's age: 2j, Equation: j + j + 6 + 2j = 42, Jenna's age: 10 years, Carl's age: 16 years, Eve's age: 20 years b) Carl's age: j - 6, Eve's age: 2j - 6, Equation: j + (j - 6) + (2j - 6) = 42, Jenna's age: 10 years, Carl's age: 16 years, Eve's age: 24 years c) Carl's age: j + 6, Eve's age: 2j - 6, Equation: j + (j + 6) + (2j - 6) = 42, Jenna's age: 10 years, Carl's age: 16 years, Eve's age: 20 years d) Carl's age: j - 6, Eve's age: 2j, Equation: j + (j - 6) + 2j = 42, Jenna's age: 10 years, Carl's age: 14 years, Eve's age: 20 years

Answer 1

Jenna's age is represented as j. Carl's age is presented as j + 6, and Eve's age is presented as 2j. After creating and solving the equation, it is found that Jenna is 9 years old, Carl is 15 years old, and Eve is 18 years old.

Step-by-step explanation:

This problem is a classic example of algebraic age problems. The problem states that Jenna, Carl, and Eve are siblings with ages that have specific relationships. We are told that Carl is 6 years older than Jenna and that Eve is twice as old as Jenna. This can be represented in terms of algebraic expressions where if j represents Jenna's age, then Carl's age will be j + 6, and Eve's age will be 2j.

Moreover, the sum of their ages is given as 42. This translates into an algebraic equation which is j (Jenna's age) + (j + 6) (Carl's age) + 2j (Eve's age) = 42. If you simplify this equation, you get 4j + 6 = 42. Solving further for j we get j = 9, which would be Jenna's age. Consequently, Carl's age would be 9 + 6 = 15 years and Eve's age would be 2 * 9 = 18 years.

Learn more about Algebraic Age Problems