SOLUTION: marilyn is three years younger than her friend rosie. in seven years the product of their ages will be 2 less than six times the product of their ages five years ago. how ald are e

Question 567656: marilyn is three years younger than her friend rosie. in seven years the product of their ages will be 2 less than six times the product of their ages five years ago. how ald are each at present
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Present age of Marilyn = m
Present age of Rosie = r

Marilyn is three years younger than her friend Rosie
m=r-3..............(1)
Five years ago
Age of Marilyn was = m-5
Age of Rosie was = r-5
In seven years
Age of Marilyn will be = m+7
Age of Rosie will be = r+7
THEN
In seven years the product of their ages will be 2 less than six times the product of their ages five years ago.
(m+7)(r+7)=6[(m-5)(r-5)]-2
mr+7m+7r+49=6(mr-5m-5r+25)-2
mr+7m+7r+49=6mr-30m-30r+150-2
mr-6mr+7m+30m+30r+7r=150-2-49
-5mr+37m+37r=150-51
-5mr+37m+37r=99..................(2)
Put the value of m from (1) to (2)
-5(r-3)r+37(r-3)+37r=99
-5r^2+15r+37r-111+37r=99
-5r^2+89r-99-111=0
-5r^2+89r-200=0
Now solve for r

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=3721 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.8, 15. Here's your graph:

r=15 or r = 2.8 (reject)
Put r=15 in (1)
m=r-3
m=15-3
m=12

Present age of Marilyn = m = 12 years old
Present age of Rosie = r = 15 years old

Check
======
Five years ago
Age of Marilyn was = 7
Age of Rosie was = 10
In seven years
Age of Marilyn will be = 19
Age of Rosie will be = 22
THEN
In seven years the product of their ages will be 2 less than six times the product of their ages five years ago.
19*22=6(7*10)-2
418=6(70)-2
418=420-2
418=418

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