Question

In figures I and II above, two stacks of identical carpenter's sawhorses are shown, with heights of 92 and 60 inches, respectively. The height , in inches, of a stack of k sawhorses is given by the function $h\left(k\right)=16k+12$, where k is a positive integer and $k\ge 1$. The dimension of which of the following in Figure III can be equal to 12?

• A. The height of one sawhorse
• B. The distance from the bottom of one sawhorse to the bottom of her next highest sawhorse
• C. The distance from the top of one sawhorse to the bottom of the next highest sawhorse
• D. The width of a sawhorse at the top

Answer 1

The correct option is C The distance from the top of one sawhorse to the bottom of the next highest sawhorse

Eliminate (D) because the entire question is about finding the height, and (D) has nothing to do with height. The difference between the left and middle stacks is $2$ stacked sawhorses. The height added to the stack of sawhorses by adding two to the stack can therefore be calculated as $92-60=32$. Therefore, the added height of one stacked sawhorse is $32÷2=16$. From this information, keep subtracting the $16$ inches added to the top of a stack by each additional sawhorse until you get down to one sawhorse in the stack. If three sawhorses are $60$ inches tall, two will be $60-16=44$ inches tall and one sawhorse will be $44-16=28$ inches tall. Choice (A), the height of one sawhorse, can now be eliminated. Another way to think about the height added to the stack of sawhorses by each additional sawhorse is to think of it as the distance between the top of one sawhorse and the top of the next. Since all the sawhorses are the same height, this distance is also the distance from the bottom of one sawhorse to the bottom of the next. Since this distance is $16$, eliminate (B). Therefore, the answer must be (C). The height of one sawhorse is $28$, which is b+c , so the overlap, c, is $28-16=12$.