Question

What number must replace x
and y
for the three fractions to become equivalent?

614 = x7 = 24y


(1 point)
x =

, y =

Remaining Attempts : 2

Answer 1

To solve for \(x\) and \(y\) in the equation \(614 = x7 = 24y\), we need to make the fractions equivalent.

We'll start by breaking down the relationships given:

1. **For \(x7\)**:
- This implies \(x7\) can be interpreted as a two-digit number where \(x\) is in the tens place. Hence, \(x7 = 10x + 7\).
- This means \(10x + 7 = 614\).

Solving for \(x\):
\[
10x + 7 = 614
\]
\[
10x = 614 - 7
\]
\[
10x = 607
\]
\[
x = \frac{607}{10} = 60.7
\]

This does not yield a valid integer for \(x\). Let's continue with the second fraction.

2. **For \(24y\)**:
\[
24y = 614
\]

Solving for \(y\):
\[
y = \frac{614}{24}
\]
\[
y = 25.5833 \, (\text{approximately})
\]

Since both \(x\) and \(y\) should yield integers for the fractions to be equivalent:

Let's equate \(x7\) and \(24y\):

From \(614 = x7\):
\[
10x + 7 = 614 \implies 10x = 607 \implies x = 60.7
\]

This is not valid for \(x\). Instead, recheck equivalency via LCM or proportions:

1. Setting up \(614 = x7\) and \(614 = 24y\) will yield proportions:
- \(x7 = \frac{614}{x}\) and \(24y = \frac{614}{y}\).

Thus analyze their ratios an solve through:

1. Equate as true fractions:
\[
\frac{614}{x7} = \frac{614}{24y}
\]

This shows \(x7 = 24y\), hence solving equivalently gives:

If \(614 = 10x + 7\) for digits, and \(614 = 24y\).

After resolving clearly:

From \(x7 \implies x = 6\), and from \(24y \implies y = 25\).

Thus, fill finalized:

So checking and carefully sufficing within logical integer values:

Final solution gives:
\[
x = 60, y = 25
\]