Quadratic equation Question?

Question

The difference of a mother's age and her daughter's age is 21 years and the twelfth part of the product of their ages is less than the mother's age by 18 years. Find their ages..... please show the working too!

Answer 1

Let y be the age of the daughter

y + 21 = Mother's age

Product = y(y+21)
1/12 of this
is less by 18 yrs from the mother's age....so...

y+21 - y(y+21)/12 = 18

12(y+21)-y^2 - 21y = 18*12

Rearrange...
0 = y^2 + 9y - 36
y = 3 and -12

since age cannot be negative answer is 3

Daughter is 3yrs old
Mother is 24 yrs old

3 * 24 / 12 = 6 which is 18 less than 24...
So that is the answer with verification

Answer 2

Let the mother's age be denoted by M, and the daughter's age by D. Common sense tells us that the mother has to be older than the daughter. Hence, the first condition tells us that
M - D = 21
The second condition tells us that
M*D/12 = M - 18

From the first equation, substitute D = M - 21 in the second one.
This gives us
M*(M - 21)/12 = M - 18

Simplifying this, gives us the following quadratic equation
M^2 - 33M + 216 = 0
Factorizing this equation gives us
(M - 24)(M-9) = 0
Hence, the mother should be either 24 years old or 9 years old. She can't be 9 cos her daughter would have a negative age... Hence the mother is 24 and the daughter is 24-18 = 6 years old..

Answer 3

Let m = mother's age.
Let d = daughter's age.
m - d = 21
(1/12) md = m - 18
Multiplying by 12 gives
md = 12m - 216
Factoring the m gives
m(d - 12) = -216
Substituting m from the first equation gives
(21 + d) (d -12 ) = -216
FOIL'ing gives
21d - 252 +d^2 - 12d = -216
Combining like terms gives
d^2 + 9d - 36 = 0
Using the quadratic formula gives
d = 3, -12.
Since age can't be negative, we take d = 3.
m = 21 + 3 = 24
Answer: The mother is 24 years old. The daughter is 3 years old.

Answer 4

x -> daughter y y->mother

y - x = 21 => x = y-21
xy/12 = y - 18 => xy = 12y - 12*18

(y-21)y = 12y - 216
y^2 -33y +216 = 0
y= {33 +- (33^2-4*216)}/2 = (33+-15)/2 = 24, 16
But only 24 is acceptable since the mother's age should be bigger than 21. So the daughter's age is 3.

Answer 5

It is, after all, your homework.

Ma =Da + 21

(Ma*Da)/12 = Ma - 18

Since Ma = Da + 12, then substitute everywhere in the second expression where you see Ma, put (Da + 21).

So (Da+21)*Da/12 = (Da+21)-18
(Da+21)*Da/12 = Da+3...........

Multiply both sides by 12 to cancel out the 12 on the left side.
And then multiply through by Da on the left side and 12 on the right side.

Da^2 + 21Da = 12Da +36

Collect like terms on the left side and get formula as expression equal to zero.

Da^2 + 9Da - 36 = 0

use Quadratic to solve.

Daughter's age can only be 3yrs old.

Recalling

Ma = Da + 21 = 3 + 21 = 24 yrs old.

Answer 6

x= Mother's age
x-21 = daughter's age
x(x-21)/12 = x - 18
x^2 -21x = 12(x-18) = 12x - 216
x^2-33x +216 = 0
x = [33 +/- sqrt(33^2-4(1)(216)]/2
x = [33 +/- 15]/2
x = 24
x = 9 which is rejected as too young
So mother = 24 .
daughter = 3

Check:
Product of ages = 72
1/12 product of ages = 6
6 is 18 < 24

Answer 7

Set up teo equations:

x-y=21
1/12*x*y=x-18

solve first eqn for y: y=x-21
Subb. into 2nd eqn.: 1/12*x*(x-21)=x-18
solve for x: x^2-33x+216=0
quddratic eqn. roots 24 and 9

only 24 makes sense so mom is 24 daughter is 3

Answer 8

x = mothers age
y = daughters age

x - y = 21
(xy)/12 = x - 18

I'm sure you can take it from there...