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?

1. 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?
2. 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.
after completing the worksheet, graph your model.
(there is a chart and a graph below with the chart having columns: quantity name (number of stairs, times katie trips), unit (stairs, times), and rows: question 1, question 2, question 3. the graph is titled times katie trips with number of stairs on the y - axis and times katie trips on the x - axis.)

Explanation:

Question 1

Step1: Understand the ratio

Katie trips once every 7 stairs. So the number of trips is the total stairs divided by 7 (since for every 7 stairs, 1 trip).

Step2: Calculate trips for 119 stairs

We have total stairs \( n = 119 \). The number of trips \( t=\frac{119}{7} \)
\( \frac{119}{7}=17 \)

Step1: Understand the ratio

Same ratio: 1 trip per 7 stairs. Total stairs \( n = 98 \)

Step2: Calculate trips for 98 stairs

Number of trips \( t=\frac{98}{7} \)
\( \frac{98}{7} = 14 \)

Step1: Define variable

Let \( x \) be the number of times Katie climbs stairs, and \( y \) be the number of trips.

Step2: Find the relationship

Since 1 trip per 7 stairs, for \( x \) stairs, trips \( y=\frac{x}{7} \)
When \( x = 16\times7=112 \) (wait, no, the problem says "wiped out for the 16th time". Wait, maybe misinterpretation. Wait, the problem says "how many stairs did she climb today? She wiped out for the 16th time." So trips = 16, so stairs \( x=7\times16 = 112 \)
Wait, re - reading: "Katie just wiped out for the 16th time. How many stairs did she climb today?"
Since 1 trip per 7 stairs, so stairs \( = 7\times \text{number of trips} \)
Number of trips = 16, so stairs \( = 7\times16=112 \)

Answer:

17

Question 2