Question 5 The oldest child in a family of four children is twice as old as the yougest. The two middle children are 12 , and 16 years old. If the average age of the children is \( \mathbf{1 3} \), how old is the youngest child? Your answer is: \( > \) Next Question
Upstudy AI Solution
Answer
Solution
Answered by UpStudy AI and reviewed by a Professional Tutor


The Deep Dive
To solve this, we first note that there are four children. The average age is 13, which means the total age of all children is \( 4 \times 13 = 52 \). We know the ages of the two middle children: 12 and 16. So we can add these together: \( 12 + 16 = 28 \). Let’s denote the age of the oldest child as \( x \) and the youngest child as \( y \). According to the information given, we have: 1. \( x + y + 28 = 52 \) (total age equation) 2. \( x = 2y \) (the oldest child is twice as old as the youngest) Substituting \( x \) from the second equation into the first gives us: \[ 2y + y + 28 = 52 \] Combine like terms: \[ 3y + 28 = 52 \] Now, subtract 28 from both sides: \[ 3y = 24 \] Dividing by 3 gives: \[ y = 8 \] So, the youngest child is 8 years old! Fun fact: Being the youngest in a family can sometimes mean you learn things faster from your older siblings—after all, you get to cheat a little by observing them! And speaking of averages, did you know that average age calculations can be influenced by just one age? If you added a baby to the mix, the average would drop, so families with little ones often find themselves feeling a bit younger collectively!