Sure, let's address each part of the question step-by-step:
b) The ratio of the ages of a mother and her son is 9:4 and the mother is 54 years old.
(i) In the given ratio which is the term that represents the mother's age?
The ratio given is 9:4. The first term (9) represents the mother's age, and the second term (4) represents the son's age.
(ii) Find the age of the son.
To find the son's age, we use the given ratio. The total parts of the ratio add up to 9 (for the mother) + 4 (for the son) = 13 parts. Since the mother's age is 54 years (which corresponds to 9 parts of the ratio), we can find the value of one part of the ratio:
[tex]\[ \text{Value of one part} = \frac{\text{Mother's age}}{9} = \frac{54}{9} = 6 \][/tex]
So, each part of the ratio equals 6 years. The son's age, being 4 parts of the ratio, is:
[tex]\[ \text{Son's age} = 4 \times 6 = 24 \text{ years} \][/tex]
(iii) What will be the ratio of the age of the mother and the son after 6 years?
To find the future ages, we add 6 years to the current ages:
- Mother's future age: [tex]\( 54 + 6 = 60 \)[/tex] years
- Son's future age: [tex]\( 24 + 6 = 30 \)[/tex] years
Now, let's find the new ratio of their ages:
[tex]\[ \text{New ratio} = \frac{\text{Mother's future age}}{\text{Son's future age}} = \frac{60}{30} = 2 \][/tex]
The new ratio of the mother's age to the son's age after 6 years will be 2:1.
