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andreyandreev [35.5K]
2 years ago
5

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 p

roduct 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​
Mathematics
1 answer:
Allisa [31]2 years ago
3 0

Step-by-step explanation:

Given

q + p = 2(q - p)

as equation 1.

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

Also given,

qp = 675

as equation 2.

Using equation 2,

q =  \frac{675}{p}

substitute this equation into equation 1.

\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

Substitute P into equation 2.

15q = 675 \\ q = 675 \div 15 \\  = 45

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

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