Consider a line segment AB of length 9 cm, which is
divided into two line segments of length 3 cm and 6 cm, as shown in the
diagram.
That is, AP = 3 cm and BP = 6 cm.
Conversely, if we know that the point P divides the line segment
AB of length 9 cm in the ratio
1 : 2, we can determine the lengths of AP and BP as follows:
So, the lengths of AP and BP are 3 cm and 6 cm,
respectively.
Check:
3 cm + 6 cm = 9 cm
Example 3
Anne and Allen worked together on a project and received $250 for their
completed work. Allen worked for 2 days and Anne worked for 3 days, and
they agree to divide the money between them in the ratio 2 : 3. How much
should each receive?
Solution:
We picture the $250 divided into equal parts.
Now, there are 5 parts and the smaller amount is 2 of them.
So, the smaller amount (Allen's share) is $100, and so Anne's share is $250
–
$100 = $150.
Example 4
An urn contains red and black marbles in the ratio 2 : 3. If
there are 40 red marbles, find the total number of marbles in the urn.
Solution:
Ratio of red marbles to black marbles = 2 : 3
Number of red marbles (2 parts out of 5) = 40
Let x be the number of marbles in the urn.
Hence the number of marbles in the urn is 100.
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