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help ?

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

614 = x7 = 24y


(1 point)
x =

, y =

1 answer

To solve the problem, we need to find the values of \( x \) and \( y \) such that the three fractions \( \frac{6}{14}, \frac{x}{7}, \frac{24}{y} \) are equivalent.

First, let's simplify the fraction \( \frac{6}{14} \):

\[ \frac{6}{14} = \frac{3}{7} \]

Now, we want to set the other fractions equal to \( \frac{3}{7} \).

  1. Finding \( x \):

Set \( \frac{x}{7} = \frac{3}{7} \).

To solve for \( x \): \[ x = 3 \]

  1. Finding \( y \):

Set \( \frac{24}{y} = \frac{3}{7} \).

Cross-multiply to solve for \( y \): \[ 3y = 24 \cdot 7 \] Calculating \( 24 \cdot 7 \): \[ 24 \cdot 7 = 168 \] So, \[ 3y = 168 \] Dividing both sides by 3 gives: \[ y = \frac{168}{3} = 56 \]

Therefore, the answers are: \[ x = 3, \quad y = 56 \]