SOLUTION: Grace is twice Bel's age 10 years ago, the square of Bel's age was 14 more than Grace's age. what is Grace age. Pls show me the solutions and represenations... Thank you very much

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Question 624177: Grace is twice Bel's age 10 years ago, the square of Bel's age was 14 more than Grace's age. what is Grace age. Pls show me the solutions and represenations... Thank you very much :)
Answer by Maths68(1474) About Me  (Show Source):
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Let
Present age of Bel = b years old
Present age of Grace = g years old
Grace is twice Bel's age.
g=2b..........(1)

10 years ago
Bel was = b-10
Grace was = g-10

Then

The square of Bel's age was 14 more than Grace's age.
(b-10)^2=(g-10)+14
b^2-20b+100=g-10+14
b^2-20b+100=g+4..................(2)
Put the value of g from (1) to (2)
b^2-20b+100=2b+4
b^2-20b+100-2b-4
b^2-22b+96=0
Now Solve for b
b^2-16b-6b+96=0
b(b-16)-6(b-16)=0
(b-16)(b-6)=0
b-16= 0 or b-6=0
b=16 or b=6

Bel's age either 16 or 6,
here we are taking her age 10 years ago
so it cannot be 6, therefore present age of Bel is 16 years old

Put the vaule b=16 in equation (1)
g=2b
g=2(16)
g=32

so
Grace is 32 years old.


Present age of Bel = b = 16years old
Present age of Grace = g = 32 years old

Ten years ago Bel was 6 years old and Grace was 22. Square of Bel age is 36 which is 14 more than Grace age (22).