Question

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

614 = x7 = 24y


(1 point)
x =

, y =

Remaining Attempts : 3
Skip to navigation

Answer 1

To make the fractions \( \frac{614}{1} \), \( \frac{x}{7} \), and \( \frac{24}{y} \) equivalent, we can set up the following equations based on the property of equivalent fractions:

1. \( \frac{614}{1} = \frac{x}{7} \)
2. \( \frac{614}{1} = \frac{24}{y} \)

**Step 1: Solve for \( x \)**

Using the first equation:
\[
614 = \frac{x}{7}
\]

Multiply both sides by 7:
\[
x = 614 \times 7
\]

Calculating \( x \):
\[
x = 614 \times 7 = 4298
\]

**Step 2: Solve for \( y \)**

Using the second equation:
\[
614 = \frac{24}{y}
\]

Cross-multiply:
\[
614y = 24
\]

Now, divide both sides by 614:
\[
y = \frac{24}{614}
\]

Since this fraction can be simplified, we can reduce it:
\[
y = \frac{12}{307}
\]

So the values of \( x \) and \( y \) that make the three fractions equivalent are:
\[
x = 4298, \quad y = \frac{12}{307}
\]

You can leave \( y \) as \( \frac{12}{307} \) or continue simplifying it in numerical form, but for clarity, we will keep it in fractional form.

**Final Answer:**
\[
x = 4298, \quad y = \frac{12}{307}
\]