Question

The basketball gym at Zane'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. Zane convinced some local businesses to match a fraction of the families' donations.
This table shows the 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)
$20 $11
$40 $22
$60 $33
$100 $55
According to the values in the table, do x and y have a proportional relationship?
yes
no

Answer 1

To determine if the values of \( x \) (the amount of money a family donates) and \( y \) (the matching contribution from local businesses) have a proportional relationship, we can check if the ratio \( \frac{y}{x} \) is constant for all the given pairs of \( (x, y) \).

Let's calculate the ratios:

1. For \( x = 20 \), \( y = 11 \):
\[
\frac{y}{x} = \frac{11}{20} = 0.55
\]

2. For \( x = 40 \), \( y = 22 \):
\[
\frac{y}{x} = \frac{22}{40} = 0.55
\]

3. For \( x = 60 \), \( y = 33 \):
\[
\frac{y}{x} = \frac{33}{60} = 0.55
\]

4. For \( x = 100 \), \( y = 55 \):
\[
\frac{y}{x} = \frac{55}{100} = 0.55
\]

Since the ratio \( \frac{y}{x} \) is constant at \( 0.55 \) for all pairs, we conclude that there is a proportional relationship between \( x \) and \( y \).

Therefore, the answer is:
**Yes.**