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Question 1098558: A,B,C and D are four points marked in order on a line such that AB:AC=3:5 and BD:CD=7:2. If CD is 10 cm long, find the length of AB.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
If AB:AC = 3:5, then AB:BC = 3:(5-3) = 3:2.
If BD:CD = 7:2, then BC:CD = (7-2):2 = 5:2.
Each of those ratios involves BC. You want to express each ratio as an equivalent ratio, by multiplying each ratio by some constant, so that the numbers for BC in both ratios are the same.
The numbers representing BC in the two ratios are 2 and 5. So multiply the first ratio by 5 and the second one by 2, to make BC=10 in both ratios:
AB:BC = 15:10; BC:CD = 10:4
Then, with the numbers for BC the same, you can combine the ratios into a single statement:
AB:BC:CD = 15:10:4
This shows you that AB:CD = 15:4. So if CD=10, AB is 10*(15/4) = 150/4 = 75/2 = 37.5.
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