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, let's assign variables to the unknowns. Let's say the shorter segment measures x inches, and the longer segment measures y inches.
We know from the problem statement that the longer segment is 15 inches longer than the shorter segment, so we can express this as:
y = x + 15
The problem also tells us that the two segments are in a ratio of 4 to 7. This means that the ratio of the longer segment to the shorter segment is 7:4, or:
y/x = 7/4
Now we have a system of two equations with two variables. We can solve it using substitution or elimination.
Since we have an equation for y in terms of x (y = x + 15), we can substitute this expression into the second equation:
(x + 15)/x = 7/4
To get rid of the fractions, we can 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
Now, substitute this value back into either of the original equations to find y:
y = x + 15
y = 20 + 15
y = 35
Therefore, the shorter segment measures 20 inches, and the longer segment measures 35 inches.
See:
http://www.jiskha.com/display.cgi?id=1299122593