a line segment is divided into two segments that are in a ratio 4 to 7. the measure of one segment is 15 inches longer than the measure of the other. Find the measure of each segment.

X/Y = 4/7 or y = 7x/4

y = X + 15
7X/4 = X + 15 or 7X = 4X + 60
3X = 60 making X = 20 and Y = 35.

Let's assume the length of the shorter segment of the line is 'x' inches.

According to the given information, the longer segment is 15 inches longer than the shorter segment. Therefore, the length of the longer segment can be expressed as 'x + 15' inches.

The ratio of the longer segment to the shorter segment is given as 7:4. Thus, we can set up the following equation:

(x + 15)/x = 7/4

To solve for x, we can cross-multiply:

4(x + 15) = 7x

Now, let's distribute the 4 on the left side:

4x + 60 = 7x

Next, subtract 4x from both sides of the equation:

60 = 7x - 4x

Combine like terms:

60 = 3x

Finally, divide both sides by 3 to isolate x:

x = 60/3

Simplifying:

x = 20

Therefore, the length of the shorter segment is 20 inches.

To find the length of the longer segment, we can substitute this value back into the equation:

x + 15 = 20 + 15
= 35

Hence, the length of the longer segment is 35 inches.

To solve this problem, let's assign variables to the lengths of the line segments. Let's call the length of the shorter segment "x" and the length of the longer segment "y".

Given that the ratio of the two line segments is 4 to 7, we can set up the equation:

x/y = 4/7 ---(1)

We are also given that one segment is 15 inches longer than the other, so we can set up another equation:

y = x + 15 ---(2)

Now, we can solve this system of equations to find the values of x and y.

First, let's rewrite equation (2) to solve for x:

x = y - 15

Now substitute this expression for x in equation (1):

(y - 15) / y = 4/7

Now we can cross-multiply:

7(y - 15) = 4y

Expand the equation:

7y - 105 = 4y

Move all the y terms to one side and the constant terms to the other side:

7y - 4y = 105

3y = 105

Divide both sides of the equation by 3:

y = 105 / 3

y = 35

Now substitute this value of y back into equation (2) to find x:

x = 35 - 15

x = 20

Therefore, the measure of the shorter segment (x) is 20 inches, and the measure of the longer segment (y) is 35 inches.