Year 10 Interactive Maths - Second Edition

Dividing a Quantity in a Given Ratio

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.