figuring out the age

**Judi** · July 6th 2006, 01:09 PM

Maria is 6 times as old as Tina. In 20 years, Maria will be only twice as old as Tina. How old is Maria now?

**Quick** · July 6th 2006, 01:23 PM

Originally Posted by Judi

Maria is 6 times as old as Tina. In 20 years, Maria will be only twice as old as Tina. How old is Maria now?

I find the easiest way to do a problem is to write everything mathematically.

first, define your variables...
$M=\text{Maria}$
$T=\text{Tina}$

Next, write out what you know.

Right now Maria is 6 times as old as Tina, therefore... $M=6T$

In 20 years Maria will only be twice as old as Tina, therefore... $M+20=2(T+20)$

Now we solve both equations for $T$

$M=6T\quad\rightarrow\quad \frac{M}{6}=T$

$M+20=2(T+20)\quad\rightarrow\quad M+20=$ $2T+40\quad\rightarrow\quad M+20-$ $40=2T\quad\rightarrow\quad \frac{M-20}{2}=T$

Now we combine the two equations...

$\frac{M}{6}=\frac{M-20}{2}$ multiply by 6

$M=\frac{6(M-20)}{2}$ extend...

$M=\frac{3\cdot\not2(M-20)}{\not2}$ multiply by 3

$M=3M-60$ subtract $3M$ from both sides...

$M-3M=-60\quad\rightarrow\quad-2M=-60\quad\rightarrow\quad \boxed{M=30}$

Voila!

**Judi** · July 6th 2006, 02:00 PM

Thank you,
Judi

**Soroban** · July 6th 2006, 02:02 PM

Hello, Judi!

Here's another approach . . . with one variable.

Maria is 6 times as old as Tina.
In 20 years, Maria will be only twice as old as Tina.
How old is Maria now?

Let $x$ = Tina's age.

Since Maria's age is 6 times Tina's age,
. . then $6x$ = Maria's age.

In 20 years, they will both be 20 years older.
. . Tina will be $x + 20$ years old.
. . Maria will be $6x + 20$ years old.

In the future, Maria's age is twice Tina's age.
. . . . . . . . . . . . . . $\downarrow\qquad\;\downarrow\quad\downarrow\qquad \,\downarrow$
. . . . . . . . . . . . $6x + 20 \;\;=\;\;2\cdot (x + 20)$

And there is your equation . . . go for it!

**Judi** · July 6th 2006, 02:11 PM

You guys are awesome!!!

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