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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

Ask by Gough Byrd. in the United States
Mar 10,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The youngest child is 8 years old.

Solution

**Step 1:** Let the age of the youngest child be \( x \). Then, since the oldest child is twice as old as the youngest, its age is \( 2x \). **Step 2:** The ages of the four children are: - Youngest: \( x \) - Second child: \( 12 \) - Third child: \( 16 \) - Oldest: \( 2x \) **Step 3:** The average age of the children is given as \( 13 \). The formula for the average age is: \[ \frac{x + 12 + 16 + 2x}{4} = 13 \] **Step 4:** Simplify and solve the equation: \[ \frac{3x + 28}{4} = 13 \] Multiply both sides by 4: \[ 3x + 28 = 52 \] Subtract 28 from both sides: \[ 3x = 24 \] Divide by 3: \[ x = 8 \] **Answer:** The youngest child is \( 8 \) years old.

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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!

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