2008 AMC 8 Problems/Problem 13

Problem

Mr. Harman needs to know the combined weight in pounds of three boxes he wants to mail. However, the only available scale is not accurate for weights less than $100$ pounds or more than $150$ pounds. So the boxes are weighed in pairs in every possible way. The results are $122$ , $125$ and $127$ pounds. What is the combined weight in pounds of the three boxes?

$\textbf{(A)}\ 160\qquad \textbf{(B)}\ 170\qquad \textbf{(C)}\ 187\qquad \textbf{(D)}\ 195\qquad \textbf{(E)}\ 354$

Solution 1

Each box is weighed twice during this, so the combined weight of the three boxes is half the weight of these separate measures:

$\frac{122+125+127}{2} = \frac{374}{2} = \boxed{\textbf{(C)}\ 187}.$

Solution 2

Using variables $a$ , $b$ , and $c$ to denote the boxes, with $a \le b \le c$ . It is obvious that $a+b=122$ and $a+c=125$ , since these are the two smallest pairs. Subtracting the former equation from the latter results in $c-b=3$ . Additionally, $c+b=127$ . Solving for $c$ and $b$ gives $c=65$ and $b=62$ , so we can thus find $a=60$ . Solving $60+62+65=\boxed{\textbf{(C) }\ 187}$

~megaboy6679

Video Solution

https://www.youtube.com/watch?v=LKhOV9p4WiY ~David

2008 AMC 8 (Problems • Answer Key • Resources)
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All AJHSME/AMC 8 Problems and Solutions

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2008 AMC 8 Problems/Problem 13

Contents

Problem

Solution 1

Solution 2

Video Solution

See Also