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.