Question

What number must replace x
and y
for the three fractions to become equivalent? 1/=x/7=24/7

Answer 1

To find the number that must replace x, we can set up the equation:

1/x = 24/7

To solve for x, we can cross multiply:

7 = 24 * x

To isolate x, we divide both sides of the equation by 24:

x = 7 / 24

Therefore, x must be replaced by 7/24.

To find the number that must replace y, we can set up the equation:

x/7 = 24/y

To solve for y, we can cross multiply:

x * y = 24 * 7

To isolate y, we divide both sides of the equation by x:

y = (24 * 7) / x

Since we already found that x = 7/24, we can substitute this value into the equation:

y = (24 * 7) / (7/24)

To divide by a fraction, we can multiply by its reciprocal:

y = (24 * 7) * (24/7)

Canceling out the common factors:

y = 24 * 24

Simplifying:

y = 576

Therefore, y must be replaced by 576.