The sum of the ages of father and son at pres | vedclass

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(B) Let the present age of the father be $F$ and the son be $S$.Given: $F + S = 33 \Rightarrow F = 33 - S$.Two years ago, their ages were $(F - 2)$ an

Vedclass · Accepted Answer

$30, 3$

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(B) Let the present age of the father be $F$ and the son be $S$.Given: $F + S = 33 \Rightarrow F = 33 - S$.Two years ago, their ages were $(F - 2)$ and $(S - 2)$.Given: $(F - 2)(S - 2) = 28$.Substitute $F = 33 - S$ into the equation:$(33 - S - 2)(S - 2) = 28$$(31 - S)(S - 2) = 28$$31S - 62 - S^2 + 2S = 28$$-S^2 + 33S - 62 = 28$$-S^2 + 33S - 90 = 0$$S^2 - 33S + 90 = 0$Factor the quadratic equation:$(S - 30)(S - 3) = 0$So, $S = 30$ or $S = 3$.Since the son cannot be $30$ years old if the sum is $33$, we take $S = 3$.Then, $F = 33 - 3 = 30$.Therefore, the father's age is $30$ and the son's age is $3$.

The sum of the ages of father and son at present is $33 \, \text{years}$. Two years ago, the product of their ages was $28 \, \text{years}$. What is the age of the father and the son (in $\text{years}$)?

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