Question 442022
Let x and y be the lengths of the two segments.
Their ratio is 5/3 so we write this as:
x/y = 5/3
Their difference is 6 so we have:
x - y = 6 [Note that in the ratio above we let x be the larger of the two segments]
From the 1st equation we can express x in terms of y as:
x = 5/3y
Substitute this value in the 2nd equation:
5/3y - y = 6
Solve for y:
2/3y = 6
y = (3/2)6 = 9
Therefore x = (5/3)y = (5/3)9 = 15
So the lengths of the two segments are 9 and 15
Check:
Ratio = 15/9 = 5/3
Difference = 15 - 9 = 6