Question

The table below shows the amount that must be repaid, y, when x dollars are borrowed.
Amount Borrowed:
$100
$200
$500
$800

Amount Repaid:
$120
$240
$600
$960

A. y = 5/6x
B. y = 6/5x
C. y = 5/6x + 10
D. y = 6/5x + 10

Answer 1

To determine the correct equation that relates the amount borrowed \( x \) to the amount repaid \( y \), we can analyze the data given:

- When \( x = 100 \), \( y = 120 \)
- When \( x = 200 \), \( y = 240 \)
- When \( x = 500 \), \( y = 600 \)
- When \( x = 800 \), \( y = 960 \)

We can calculate the ratio \( \frac{y}{x} \) for each pair:

1. For \( x = 100 \), \( y = 120 \):
\[
\frac{y}{x} = \frac{120}{100} = 1.2
\]

2. For \( x = 200 \), \( y = 240 \):
\[
\frac{y}{x} = \frac{240}{200} = 1.2
\]

3. For \( x = 500 \), \( y = 600 \):
\[
\frac{y}{x} = \frac{600}{500} = 1.2
\]

4. For \( x = 800 \), \( y = 960 \):
\[
\frac{y}{x} = \frac{960}{800} = 1.2
\]

Since all the ratios give us \( 1.2 \), we can conclude that \( y \) is directly proportional to \( x \) with a constant of proportionality of \( 1.2 \) or \( \frac{6}{5} \).

This means:
\[
y = 1.2x \quad \text{or} \quad y = \frac{6}{5}x
\]

Among the options provided, the correct equation is:

**B. \( y = \frac{6}{5}x \)**