Question

Fill in the missing fractions to create a true equation.(1 point)
___ /5 − 12 = 3/___

Answer 1

To solve the equation, we start from:

\[
\frac{x}{5} - 12 = \frac{3}{y}
\]

First, add 12 to both sides to isolate the fraction:

\[
\frac{x}{5} = \frac{3}{y} + 12
\]

Now, let's express 12 as a fraction with a denominator of \(y\):

\[
12 = \frac{12y}{y}
\]

Thus, we can rewrite the right side:

\[
\frac{x}{5} = \frac{3 + 12y}{y}
\]

Next, we cross-multiply to eliminate the fractions:

\[
x \cdot y = 5(3 + 12y)
\]

Distributing the 5:

\[
xy = 15 + 60y
\]

Now we can rearrange this equation to isolate \(x\):

\[
xy - 60y = 15
\]

Factoring out \(y\):

\[
y(x - 60) = 15
\]

From here, we can find specific values for \(x\) and \(y\). Let's say:

1. Let \(y = 1\):
- \(1(x - 60) = 15\) → \(x - 60 = 15\) → \(x = 75\)
So, one pair is \( (75, 1) \).

2. Let \(y = 3\):
- \(3(x - 60) = 15\) → \(x - 60 = 5\) → \(x = 65\)
So, another pair is \( (65, 3) \).

3. Let \(y = 5\):
- \(5(x - 60) = 15\) → \(x - 60 = 3\) → \(x = 63\).
So, another pair is \( (63, 5) \).

Based on the pairs provided, we could replace the missing fractions in our original equation like this:

Thus, we can conclude:

\[
75/5 - 12 = 3/1
\]

or

\[
65/5 - 12 = 3/3
\]

or

\[
63/5 - 12 = 3/5
\]

All satisfy the equation, and thus the missing fractions could be represented as:

### Final Answer:
**75/5 - 12 = 3/1** (which is a valid option).

Any of the pairs will work.