Question

katie is very clumsy. she trips up one of every seven stairs she climbs.

1. if she keeps this up, how many times will katie trip if she walks up 119 stairs?
2. katie lives on the tenth floor of her apartment building and there is no elevator. she has to climb 98 stairs to get to her apartment. how many times will she trip?
3. katie just wiped out for the 16th time. how many stairs did she climb today?

enter a variable for the total number of stairs katie climbs and use this variable to write an expression for the number of times katie trips.
(there is also a chart titled times katie trips with a grid and some plotted points, and a table with question 2 (98 stairs), question 3 (112 stairs) and an expression column.)

Explanation:

Question 1

Step1: Determine the ratio

Katie trips once every 7 stairs. So the ratio of trips to stairs is \( \frac{1}{7} \).

Step2: Calculate trips for 119 stairs

Let \( t \) be the number of trips. Then \( t=\frac{119}{7} \).
\( 119\div7 = 17 \)

Step1: Determine the ratio

From the ratio (trips per stair), since trips per 7 stairs is 1, per stair is \( \frac{1}{7} \).

Step2: Calculate trips for 98 stairs

Let \( t \) be trips. \( t = \frac{98}{7} \)
\( 98\div7=14 \)

Step1: Define variable

Let \( s \) be the number of stairs Katie climbs, and \( t \) be the number of trips.

Step2: Formulate the expression

Since she trips once every 7 stairs, the expression is \( t=\frac{s}{7} \) (or \( t = \frac{1}{7}s \))
For \( s = 112 \), \( t=\frac{112}{7}=16 \) (which matches the table, verifying the expression)

Answer:

17

Question 2