# Help me in this word problems

• Sep 20th 2006, 07:24 AM
Hi888
Help me in this word problems

1. Marivic is five yrs. older than Michelle. In three yrs., the product of her age and Michelle's age five years ago will be 90. Find their present ages?

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2. Cora is twice as old as Maria. The quotient of their ages five years ago was seven less than Maria's present age. Find their present ages?

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PLEASE HELP ME IN THIS HOMEWORK! I ONLY GOT 5 HOURS TO GO BEFORE I SUBMIT THIS.

I SINCERELY THANK ALL WHO WILL HELP:)
• Sep 20th 2006, 07:35 AM
topsquark
Quote:

Originally Posted by Hi888
1. Marivic is five yrs. older than Michelle. In three yrs., the product of her age and Michelle's age five years ago will be 90. Find their present ages?

Let Marivic's age be x. Then Michelle's age is x - 5.

(This next clue is worded badly. I think this is what it means.) In three years Marivic's age is x + 3 and five years ago Michelle's age was x - 10.

Thus (x + 3)(x - 10) = 90.

x^2 - 7x - 30 = 90

x^2 - 7x - 120 = 0

(x - 15)(x + 8) = 0

So x = 15 or -8. An age of -8 is clearly ridiculous, so Marivic's present age is 15 and Michelle's present age is 15 - 5 = 10.

-Dan
• Sep 20th 2006, 07:42 AM
topsquark
Quote:

Originally Posted by Hi888
2. Cora is twice as old as Maria. The quotient of their ages five years ago was seven less than Maria's present age. Find their present ages?

Let Maria's age be x. The Cora's age is 2x. Their ages 5 years ago are: Maria's x -5 and Cora's 2x - 5. Thus:
(2x - 5)/(x - 5) = x - 7 (We HAVE to do the quotient this way, else x - 7 is less than 1.)

2x - 5 = (x - 5)(x - 7)

2x - 5 = x^2 - 12x + 35

x^2 -14x + 40 = 0

(x - 4)(x - 10) = 0

So Maria's age is either 4 or 10. Now, if Maria could be 4, then 5 years ago her age would have been -1, which is impossible. Thus Maria is 10 and Cora is 20.

-Dan