Question

finding the whole with a tape diagram

keisha can run 170 meters in one minute. this is 125% of the distance that she could run in one minute three years ago. how far could keisha run in one minute three years ago?

3 yrs. ago:
?
100%
\\(\frac{4}{4}\\)

today:
170 m
125%
\\(\frac{5}{4}\\)

\\(\frac{125}{100} = \frac{5}{4}\\)

Explanation:

🆕 New Concept Discovered: Solving Percent Problems with Tape Diagrams
Using visual blocks to find the whole from a part.

Step 1: Understand the given values and ratios

The distance Keisha can run today is \( 170\text{ m} \), which represents \( 125\% \) of the distance she could run three years ago.

We want to find the original distance (\( 100\% \)).

Convert the percentage to a simplified fraction:

$$ \frac{125}{100} = \frac{5}{4} $$

This means today's distance is represented by \( 5 \) equal units (parts) of a tape diagram, while the original distance from three years ago is represented by \( 4 \) equal units.

Step 2: Calculate the value of one unit

Since \( 5 \) units represent today's distance of \( 170\text{ m} \), we divide the total distance by the number of units to find the value of a single unit:

$$ \text{Value of 1 unit} = \frac{170}{5} = 34\text{ m} $$

Step 3: Calculate the original distance

The distance three years ago (\( 100\% \)) is represented by \( 4 \) units:

$$ \text{Original distance} = 4 \times 34 = 136\text{ m} $$

Answer:

Keisha could run 136 meters in one minute three years ago.