What number must replace x and y for the three fractions to become equivalent?
614 = x7 = 24y
To find the numbers that must replace x and y for the three fractions to become equivalent, we need to solve the equations:
614 = x/7
614 * 7 = x
4298 = x
and
614 = 24y
614 / 24 = y
25.58 ≈ y
Therefore, x must be replaced by the number 4298 and y must be replaced by the number 25.58.
To find the values of x and y that will make the fractions equivalent, we need to set up an equation for each fraction and solve for x and y.
The given fractions are 614/7 and x/24y.
To make the two fractions equivalent, their ratios must be equal. Therefore, we can set up the following equation:
614/7 = x/24y
To solve this equation, we need to cross multiply:
614 * 24y = 7 * x
14736y = 7x
Now, we can solve for x in terms of y:
x = 14736y / 7
Simplifying this expression:
x = 2105.14y
Now we have an expression for x in terms of y. However, we still need to find the specific values of x and y that make the fractions equivalent. Unfortunately, with the given information, we can't determine the exact values of x and y, but we can express x in terms of y as x = 2105.14y.
To find the number that must replace x and y to make the three fractions equivalent, we need to set up a proportion and solve for x and y. Let's break down the given equation:
We have the fractions:
614/x = 7/1
x/24 = 1/y
To solve for x, we can cross multiply:
614 * 1 = x * 7
614 = 7x
Divide both sides of the equation by 7 to isolate x:
614/7 = x
x ≈ 87.71
To solve for y, we can cross multiply again:
x * 24 = 1 * 24y
24x = 24y
Divide both sides of the equation by 24 to isolate y:
24x/24 = y
y = x
Therefore, the number that replaces both x and y to make the three fractions equivalent is approximately 87.71.