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
Ann and Allen worked together on a project and received $250 for their
completed work. Allen worked for 2 days and Ann 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. |