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1. A mother is six times as old as her son. In five years' time, the sum of their ages will be 45 years. Calculate their present ages.

(3 marks)

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(Note: No LaTeX tags were present to retain, and the ending "syrs [tex]$x=5$[/tex]" was removed as it appeared to be nonsense.)



Answer :

GinnyAnswer
Let's go through the problem step-by-step:

1. Define Variables:
- Let the son's current age be [tex]\( s \)[/tex].
- The mother's current age is then [tex]\( 6s \)[/tex] since she is six times as old as her son.

2. Set Up the Equation:
- In 5 years, the son’s age will be [tex]\( s + 5 \)[/tex].
- In 5 years, the mother’s age will be [tex]\( 6s + 5 \)[/tex].
- The sum of their ages in 5 years will be [tex]\( 45 \)[/tex].

3. Form the Equation:
- According to the problem, [tex]\( (s + 5) + (6s + 5) = 45 \)[/tex].

4. Simplify and Solve for [tex]\( s \)[/tex]:
- Combine the terms: [tex]\( s + 6s + 5 + 5 = 45 \)[/tex].
- Simplify further: [tex]\( 7s + 10 = 45 \)[/tex].
- Subtract 10 from both sides: [tex]\( 7s = 35 \)[/tex].
- Divide both sides by 7: [tex]\( s = 5 \)[/tex].

5. Find the Mother’s Age:
- The mother's age is [tex]\( 6s \)[/tex].
- Substituting [tex]\( s = 5 \)[/tex]: [tex]\( 6 \times 5 = 30 \)[/tex].

So, the son's current age is 5 years, and the mother's current age is 30 years.

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