Explanation for Question 19 From the Math (Calc) Section on the Official Sat Practice Test 6
Question 19 asks us an architect, 2 wants to use the riser tread formula to design a stairway with a total 3 rise of nine feet, a riser height between seven and eight inches and an 4 odd number of steps. So we know that we're using the riser tread formula, 5 which is what I've written right here. And that's just this formula from up 6 here, rewritten, as we did for question 17, 7 with the architect's constraints, which of the following must be the tread depth in 8 inches of the stairway. All right. 9 So it also gives us the conversion that one foot is equal to 12 10 inches, and we're going to use that first to convert the total rise into 11 inches. So nine feet, 12 you know, that there are 12 inches in one foot. 13 So in order to cancel out the units, we're going to multiply nine feet 14 by 12, cancel out the feet units and we'd get 108 15 inches. 16 So the total rise, which we're going to call R is equal 17 to 108 inches. 18 Okay. So now that we've done that, 19 we need to figure out what the next step is. 20 So we've got the total rise. We have the height of each step, 21 so height of stuff, and let's call that H and we know that H 22 has to be between seven to eight inches. 23 So those are the key pieces of information that we have for this question. 24 So thinking about going back up to this picture right here, 25 there's actually another key relationship that we know. 26 So we know that the total rise is going to be equal to the 27 riser height times the number of steps,...