What number must replace x
and y
for the three fractions to become equivalent? 6/14=x/7=24/y
x = blank
y = blank
To find the missing numbers, we can set up equations using the given information.
First, we can compare the first fraction, 6/14, with the second fraction, x/7.
6/14 = x/7
To solve for x, we can cross-multiply:
6 * 7 = 14 * x
42 = 14x
Dividing both sides by 14:
42/14 = x
3 = x
So, x = 3.
Next, we can compare the first fraction, 6/14, with the third fraction, 24/y.
6/14 = 24/y
To solve for y, we can cross-multiply:
6 * y = 14 * 24
6y = 336
Dividing both sides by 6:
336/6 = y
56 = y
So, y = 56.
Therefore, x = 3 and y = 56.
That is correct!😊
I'm glad I could help! If you have any more questions, feel free to ask.
To find the values of x and y that make the three fractions equivalent, we can set up a proportion.
First, let's set up the proportion using the first two fractions:
6/14 = x/7
To find x, we can cross multiply:
14 * x = 6 * 7
Simplifying the equation:
14x = 42
Dividing both sides by 14:
x = 42/14
Which simplifies to:
x = 3
Now let's set up the proportion using the second and third fractions:
x/7 = 24/y
Cross multiplying:
7 * 24 = x * y
168 = xy
To find y, we can divide both sides by x:
y = 168 / x
Substituting the value we found for x:
y = 168 / 3
Simplifying:
y = 56
So, x = 3 and y = 56.
To find the values of x and y that would make the three fractions equivalent, we need to set up and solve a system of equations.
First, let's set up the equation for the three fractions:
6/14 = x/7 = 24/y
Now, let's find the value of x:
We can cross-multiply the first fraction:
6 * 7 = 14 * x
42 = 14x
Divide both sides of the equation by 14 to solve for x:
42/14 = 14x/14
3 = x
Therefore, x = 3.
Now, let's find the value of y:
We can cross-multiply the second fraction:
x * 7 = 6 * 24
7x = 144
Divide both sides of the equation by 7 to solve for x:
7x/7 = 144/7
x = 144/7
Therefore, x = 144/7.
So, the final answers are:
x = 3
y = 144/7.