Question 11. The distance between two shelves in the cupboard in Monica's kitchen is 36 centimeters. She knows that a stack of eight of her favorite glasses is 42 centimeters tall and that a stack of two glasses is 18 centimeters tall. What is the largest number of glasses that can be stacked and still fit between two shelves? You can start off by labeling glass height as X, meaning the total height of one glass. Next, we can label the extra of the glass as Y, meaning the amount of height that is added when a glass is put in another glass. You can write the formula X plus Y equals 18, since we know that two glasses are 18 centimeters tall. Next, we write out the formula X plus 7Y equals 42, since we know that eight glasses stacked together is 42 centimeters. If we subtract these formulas from each other, we get 6Y equal to 24, or simplifying, Y equals 4, so we know that each additional glass beyond the first adds 4 centimeters to the height. Now we can easily find out the height of an entire glass by plugging 4 into X plus Y. When we do X plus 4 equals 18, we get X equal to 14, so a glass is 14 centimeters tall. Now we want to know how many glasses we can fit in a 36 centimeter shelf, so we do 14, which is the height of one glass, plus however many additional glasses that add 4 centimeters, so we can subtract 14 and get 22, then we divide by 4 and get 5.5, and we have to remember to add an additional glass, since we can have one glass and then add 5.5 glasses to that height. Now we cannot add half a glass, so from 6.5 we have to round down to 6, and with that we see that our answer will be D, 6.

stacking glasses

shelf space

glass height

calculate fit

tallest stack