Question

The basketball gym at Dustin'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. Dustin 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. When a family donates $12, the businesses contribute $9. Write the equation for the relationship between x and y.

Answer 1

To write the equation for the relationship between x and y, we need to determine the fractional amount of the donation that the businesses are matching. The equation for the relationship is y = (3/4)x.

Step-by-step explanation:

To write the equation for the relationship between x (the amount of money a family donates in dollars) and y (the matching contribution from local businesses in dollars), we first need to determine the fractional amount of the donation that the businesses are matching.

From the given information, when a family donates $12, the businesses contribute $9. This can be written as:

x = $12

y = $9

So, the matching contribution from the businesses is 9/12 or 3/4.

The equation for the relationship is then:

y = (3/4)x

Answer 2

The equation representing the relationship between x and y is that;

4y = 3x

Step-by-step explanation:

Here, we want to write a relationship.

From the question, we are told that the amount donated by the family which is x dollars is proportional to what local businesses gave.

From the question, there was an example in which a family gave $12 and local businesses gave $9

So let us establish a relationship using ratio of x to y

Thus;

12/9 = x/y

12y = 9x

4y = 3x