Question

The housekeeping staff at the Weary Traveler Hotel rotates job assignments every day. Today, Eli is in charge of folding the freshly cleaned bedsheets.
This table shows the relationship between the amount of time (in minutes) Eli spends folding, x, and the number of bedsheets he folds, y.
x (minutes) y (bedsheets)
3 12
15 60
16 64
23 92
According to the values in the table, do x and y have a proportional relationship?
yes
no
Write an equation for the relationship between x and y. Simplify any fractions.
y=

Answer 1

To determine whether \( x \) and \( y \) have a proportional relationship, we can check if the ratio \( \frac{y}{x} \) is constant for each pair of values.

Using the values in the table:

1. For \( x = 3 \), \( y = 12 \):
\[
\frac{y}{x} = \frac{12}{3} = 4
\]

2. For \( x = 15 \), \( y = 60 \):
\[
\frac{y}{x} = \frac{60}{15} = 4
\]

3. For \( x = 16 \), \( y = 64 \):
\[
\frac{y}{x} = \frac{64}{16} = 4
\]

4. For \( x = 23 \), \( y = 92 \):
\[
\frac{y}{x} = \frac{92}{23} = 4
\]

Since the ratio \( \frac{y}{x} \) is consistently equal to 4 for all pairs of values, we conclude that \( x \) and \( y \) do indeed have a proportional relationship.

Next, we can express this relationship as an equation. Since the ratio \( \frac{y}{x} = 4 \), we can write the equation as:

\[
y = 4x
\]

So the answer is:

**yes**, \( x \) and \( y \) have a proportional relationship.

The equation for the relationship between \( x \) and \( y \) is:

\[
y = 4x
\]