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Mathematics 23 Online
OpenStudy (anonymous):

Dorothy is 14 years younger then Rita. Ten years ago, rita was 3 times as old as dorothy was then. how old is each now? step by step plz :)

OpenStudy (anonymous):

Create two different equations. The first telling the age now in relation and the second for ten years ago. Then solve for either dorothy or rita and substitute into the other equation. Doesn't matter the order in which you choose an equation.

OpenStudy (anonymous):

would (14-x) = 10-(3-x) be correct?

OpenStudy (anonymous):

a little backwards. If I'm 23 and someone was 14 years younger than me, I would subtract 14 from my age.

OpenStudy (anonymous):

You're definitely getting there though. Lookin' good

OpenStudy (anonymous):

(x-14) = 10-(3-x)

OpenStudy (anonymous):

is that correct?

OpenStudy (anonymous):

Now, when someone is three times someone else's age, what operation are we using?

OpenStudy (anonymous):

multiplication

OpenStudy (anonymous):

I'm assuming you're using x as rita in x-14 which is correct. Good! so ten years ago rita was three times as much as dorothy

OpenStudy (anonymous):

thank you !!

OpenStudy (anonymous):

did you get the answer then?

OpenStudy (anonymous):

i got x =8

OpenStudy (anonymous):

(x-14) = 3(10-x) x-14 = 30-x 2x + 16 divide 16 by 2 and got 8

OpenStudy (anonymous):

We need present value though. 8-10 for age does not exist, so what do you need to do?

OpenStudy (anonymous):

10-8

OpenStudy (anonymous):

this is what I got R=31 and D=17. Your first equation should be D=R-14

OpenStudy (anonymous):

Sooooooo, if I wanted to represent three times an age ten years ago, I would do 3(D-10)

OpenStudy (anonymous):

So what can you do with that part now? How do you represent Rita's age ten years ago?

OpenStudy (anonymous):

10-3 = 8

OpenStudy (anonymous):

31 for rita and 17 for dorothy. Assume, x = rita y = dorothy x - y = 14, 3y = x We automatically know that since 14 is the age difference and 10 years ago y + 14 = 3y That means that 14 must be 2y because 3y - y = 2y = 14 Therefore y = 7 That means that 10 years ago the relation between rita and dorothy's age may be represented by this equation : 7 + 14 = 21 That means 10 years ago rita was 21 years old and so dorothy must have been 21-14 = 7 years old. To find current ages do the following: rita's age = 21 + 10 = 31 dorothy's age = 7+10=17

OpenStudy (anonymous):

genius, you're a slackers dream. I wish I could just come on open study and get all of my questions worked out for me.

OpenStudy (anonymous):

Well, I do appreciate working with you kelly. I hope now it is clear. If not, you know where to find me.

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