Math  /  Algebra

QuestionDarin's great aunt lives in a retirement home. Darin visits her to help plant green beans in a garden. So far they have planted 6 rows with 72 green bean stalks. They plant the same number of green bean stalks in each row.
What is the constant of proportionality in this relationship? 6 12 72 78

Studdy Solution

STEP 1

What is this asking? How many green bean stalks did Darin and his great aunt plant per row in the retirement home's garden? Watch out! Don't get tricked by the total number of stalks!
We need the number *per row*.

STEP 2

1. Find the number of stalks per row.

STEP 3

We know they planted a **total** of 7272 green bean stalks in 66 rows.
We want to find out how many stalks are in *each* row.
To do this, we'll **divide** the total number of stalks by the number of rows.
This will give us the number of stalks *per* row.
It's like figuring out how many cookies each person gets if you divide a whole box evenly!

STEP 4

So, we have 7272 stalks divided by 66 rows: 726 \frac{72}{6}

STEP 5

Let's break down the division: 66 goes into 77 **one** time with a remainder of 11.
Bring down the 22 to make 1212. 66 goes into 1212 **two** times with no remainder.
So, 726=12 \frac{72}{6} = 12 This means there are **1212** green bean stalks per row.
This 1212 is our **constant of proportionality**!
For every row they add, they add another 1212 stalks.

STEP 6

The constant of proportionality is 1212.

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