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

The relationship between the amount of money a family donates, $x$, and the matching contribution from local businesses, $y$, is proportional. This means that:

\[
y = k \cdot x
\]

Where $k$ is the constant of proportionality, representing the dollars matched per dollar donated.

To find $k$, we can use the ratio of $y$ to $x$:

\[
k = \frac{y}{x}
\]

Using any of the provided data points, let's calculate $k$.

For $x = 28$ and $y = 7$:

\[
k = \frac{7}{28} = 0.25
\]

Let's check if this holds for other data points.

For $x = 36$ and $y = 9$:

\[
k = \frac{9}{36} = 0.25
\]

For $x = 76$ and $y = 19$:

\[
k = \frac{19}{76} = 0.25
\]

For $x = 84$ and $y = 21$:

\[
k = \frac{21}{84} = 0.25
\]

Since $k = 0.25$ for all cases, the constant of proportionality is:

\[
\boxed{0.25}
\]

This means the businesses match $0.25$ dollars for every dollar donated.

Would you like further details or have any questions?

Here are 5 related questions:
1. If a family donates $100, how much will be matched by local businesses?
2. How much will local businesses match if the total family donations are $500?
3. What fraction of the family donations is being matched by the businesses?
4. If the businesses matched $50, how much did the families donate?
5. Can the relationship between donations and matching be graphed? What would the graph look like?

**Tip:** When solving proportional relationships, always check for a consistent ratio across multiple data points.

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

Learn how to calculate the constant of proportionality between family donations and matching contributions from local businesses. Explore proportional relationships and ratios with specific data points like $28 donated leading to $7 matched, and more. Suitable for students in Grades 6-8.

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