The basketball gym at Dean's school was built in the 1940s and needs a lot of repairs. So, the school is asking families for donations to build a new gym. Dean convinced some local businesses to match a fraction of the families' donations.

There is a proportional relationship between the amount of money a family donates (in dollars), 

*x*,

 and the matching contribution (in dollars) from local businesses, 

*y*.

*x* (dollars donated)

*y* (dollars matched)

$28

$7

$36

$9

$76

$19

$84

$21

What is the constant of proportionality? Write your answer as a whole number or decimal.

dollars matched per dollar donated





To find the constant of proportionality between the amount of money a family donates ($x$) and the matching contribution from local businesses ($y$), we need to determine the ratio of $y$ to $x$ for any pair of values.

From the data provided:

\[
\frac{y}{x} = \frac{7}{28} = \frac{1}{4} = 0.25
\]

This ratio is the same for all the pairs:

- $\frac{9}{36} = 0.25$
- $\frac{19}{76} = 0.25$
- $\frac{21}{84} = 0.25$

So, the constant of proportionality (dollars matched per dollar donated) is **0.25**.

Would you like more details or have any questions?

Here are 5 related questions:

1. What does the constant of proportionality represent in this context?
2. How would you use this constant to predict the matched amount if a family donates $100?
3. Can the constant of proportionality be greater than 1 in some cases?
4. How does this relationship change if the businesses match 50% of the donations instead?
5. How would you graph this proportional relationship?

**Tip:** The constant of proportionality tells you how much one quantity changes in relation to another, which is crucial in understanding proportional relationships.

The basketball gym at Dean's school was built in the 1940s and needs a lot of repairs. So, the school is asking families for donations to build a new gym. Dean convinced some local businesses to match a fraction of the families' donations. There is a proportional relationship between the amount of money a family donates (in dollars), x, and the matching contribution (in dollars) from local businesses, y. x (dollars donated) y (dollars matched) $28 $7 $36 $9 $76 $19 $84 $21 What is the constant of proportionality? Write your answer as a whole number or decimal. Dollars matched per dollar donated.

Explore how to find the constant of proportionality between family donations and business matching contributions. Learn to calculate the ratio of matched contributions to donations with real-world examples. Suitable for students in Grades 6-8.

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