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.

Use ratios

4 : 7 : 7-4=3
X : Y : 15"

Cross multiply with X:
X=4*15/3=20
Cross multiply with Y:
Y=7*15/3=35

Check: Y-X=15, Y/7=X/4=5 OK

To solve this problem, we can follow these steps:

Step 1: Assign variables
Let's assign variables to the unknowns in the problem. We'll call the shorter segment "x" and the longer segment "y", measured in inches.

Step 2: Write equations
From the problem statement, we can derive the following equations:
1. The ratio of the segments is 4:7, so we can write the equation: x/y = 4/7.
2. The longer segment is 15 inches longer than the shorter segment, so we can write the equation: y = x + 15.

Step 3: Solve the equations
Using the first equation, we can express x in terms of y by cross-multiplying:
7x = 4y.

Next, substitute the value of y from the second equation into the first equation:
7x = 4(x + 15).

Simplify and solve for x:
7x = 4x + 60,
3x = 60,
x = 20.

Step 4: Calculate the lengths of the segments
Now that we have the value of x, we can substitute it into the second equation to find the value of y:
y = x + 15,
y = 20 + 15,
y = 35.

Therefore, the measure of the shorter segment is 20 inches, and the measure of the longer segment is 35 inches.