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A woman is q years old while her son is p years old. the sum of their ages is equal to twice the difference of their ages. the product of their ages is 675.
write down the equations connecting their ages and solve the equations in order to find the ages of the woman and her son. WAEC​

Sagot :

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Step-by-step explanation:

Given

[tex]q + p = 2(q - p)[/tex]

as equation 1.

I used q-p as the difference as logically the woman will be older than her son.

Also given,

[tex]qp = 675[/tex]

as equation 2.

Using equation 2,

[tex]q = \frac{675}{p} [/tex]

substitute this equation into equation 1.

[tex] \frac{675}{p} + p = 2( \frac{675}{p} - p) \\ \frac{675}{p} + p = \frac{1350}{p} - 2p \\ \frac{675}{p} - \frac{1350}{p} = - 2p - p \\ - 3p = - \frac{675}{p} \\ - 3p \times p = - 675 \\ - 3 {p}^{2} = - 675 \\ {p}^{2} = - 675 \div - 3 \\ {p}^{2} = 225 \\ p = \sqrt{225} \\ = 15[/tex]

Substitute P into equation 2.

[tex]15q = 675 \\ q = 675 \div 15 \\ = 45[/tex]

Therefore the woman is 45 years old while her son is 15 years old.

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