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.
To solve this problem, we can assign variables to represent the lengths of the segments. Let's assume that the shorter segment has a length of x inches.
According to the information given, the longer segment is 15 inches longer than the shorter one. Therefore, the length of the longer segment is x + 15 inches.
The ratio of the lengths of the two segments is given as 4 to 7. This means that the shorter segment is 4 parts out of a total of 4 + 7 = 11 parts, and the longer segment is 7 parts out of the total.
To find the length of each segment, we can set up the following equation:
(x + 15) / x = 7 / 4
To solve this equation, we need to cross-multiply:
4(x + 15) = 7x
Distribute the 4:
4x + 60 = 7x
Subtract 4x from both sides:
60 = 3x
Divide both sides by 3:
x = 20
Therefore, the shorter segment measures 20 inches, and the longer segment measures 20 + 15 = 35 inches.