Question

The table below shows the amount that must be repaid, y, when x dollars are borrowed.

Amount Borrowed Amount Repaid
$100 $120
$200 $240
$500 $600
$800 $960
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(1 point)
Responses

y=56x
y is equal to 5 sixths x

y=65x+10
y is equal to 6 fifths x plus 10

y=56x+10
y is equal to 5 sixths x plus 10

y=65x
y is equal to 6 fifths x

Answer 1

To find the relationship between the amount borrowed \( x \) and the amount repaid \( y \), we can look for a consistent pattern or ratio in the data provided.

From the table:

- When $100 is borrowed, $120 is repaid.
- When $200 is borrowed, $240 is repaid.
- When $500 is borrowed, $600 is repaid.
- When $800 is borrowed, $960 is repaid.

If we examine the ratio of the amount repaid to the amount borrowed:

- For $100 borrowed: \( \frac{120}{100} = 1.2 \)
- For $200 borrowed: \( \frac{240}{200} = 1.2 \)
- For $500 borrowed: \( \frac{600}{500} = 1.2 \)
- For $800 borrowed: \( \frac{960}{800} = 1.2 \)

We can see that the amount repaid is consistently 1.2 times (or \( \frac{6}{5} \) times) the amount borrowed.

Thus, we can express the relationship as:

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

Among your options, the equation that matches this relationship is:

**y is equal to 6 fifths x**

So, that is the correct answer: **y = 6/5 x**.