Question: Top-left: The expression is $\frac{x+y+5}{2}$, with the numerator over 2.
Justin's doctor said that the expression $\frac{x+y+5}{2}$, where $x$ and $y$ are his parents' current heights in inches, gives an estimate of how tall Justin will be as an adult. Justin’s work evaluating the formula is shown below.
Mom’s height = 54 inches
Dad’s height = 71 inches
$$\frac{71+54+5}{2} = 71+27+5 = 103 \text{ inches}$$
What error did Justin make?
○ He should have made $x$ equal 54 and $y$ equal 71.
○ He should have added the values in the numerator before dividing by 2.
○ He should have divided the 71 by 2 instead of the 27.
○ He should have made the numerator 76 + 59.
1. **State the problem:** Justin is using the formula $$\frac{x+y+5}{2}$$ to estimate his adult height, where $x$ and $y$ are his parents' heights.
2. **Given values:** Mom's height $= 54$ inches, Dad's height $= 71$ inches.
3. **Justin's calculation:** He wrote $$\frac{71+54+5}{2} = 71 + 27 + 5 = 103$$ inches.
4. **Identify the error:** The formula requires adding the numerator first, then dividing by 2.
5. **Correct calculation:**
$$\frac{71 + 54 + 5}{2} = \frac{130}{2} = 65$$ inches.
6. **Explanation:** Justin incorrectly split the division and added terms after dividing only part of the numerator, which is mathematically incorrect.
7. **Conclusion:** The correct step is to add all terms in the numerator before dividing by 2.
**Final answer:** Justin should have added the values in the numerator before dividing by 2.