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Cheryl is 3/5 as old as her mum. In 8 years time, the ratio of her age to her mom's age will be 2:3. How old is Cheryl now??

 Aug 17, 2015

Best Answer 

 #1
avatar+26364 
+10

Cheryl is 3/5 as old as her mum. In 8 years time, the ratio of her age to her mom's age will be 2:3. How old is Cheryl now??

 

m = mum      c = cheryl

 

(1) $$c = \frac 35 m \qquad \text { or } \qquad m = \frac 53 c$$

(2) $$\frac{c+8}{m+8} = \frac 23 \qquad \text{ or } \qquad c = \frac 23 \cdot (m+8) - 8$$

 

$$\small{\text{$
\begin{array}{lcl}
c &=& \frac 23 \cdot (m+8) - 8 \qquad | \qquad m=\frac 53 c\\\\
c &=& \frac 23 \cdot (\frac 53 c+8) - 8 \\\\
c &=& \frac {10}{9} c + 8\cdot \frac 23 - 8 \\\\
c &=& \frac {10}{9} c + \frac {16}{3} - 8 \qquad | \qquad \cdot 9\\\\
9c &=& 10 c + 3\cdot 16 - 72\\\\
9c &=& 10 c -24\\\\
10c - 9 c &=& 24\\\\
\mathbf{c} & \mathbf{=} & \mathbf{24}\\
\end{array}
$}} \\\\$$

 

Cheryl is now 24 years old

 

 Aug 17, 2015
 #1
avatar+26364 
+10
Best Answer

Cheryl is 3/5 as old as her mum. In 8 years time, the ratio of her age to her mom's age will be 2:3. How old is Cheryl now??

 

m = mum      c = cheryl

 

(1) $$c = \frac 35 m \qquad \text { or } \qquad m = \frac 53 c$$

(2) $$\frac{c+8}{m+8} = \frac 23 \qquad \text{ or } \qquad c = \frac 23 \cdot (m+8) - 8$$

 

$$\small{\text{$
\begin{array}{lcl}
c &=& \frac 23 \cdot (m+8) - 8 \qquad | \qquad m=\frac 53 c\\\\
c &=& \frac 23 \cdot (\frac 53 c+8) - 8 \\\\
c &=& \frac {10}{9} c + 8\cdot \frac 23 - 8 \\\\
c &=& \frac {10}{9} c + \frac {16}{3} - 8 \qquad | \qquad \cdot 9\\\\
9c &=& 10 c + 3\cdot 16 - 72\\\\
9c &=& 10 c -24\\\\
10c - 9 c &=& 24\\\\
\mathbf{c} & \mathbf{=} & \mathbf{24}\\
\end{array}
$}} \\\\$$

 

Cheryl is now 24 years old

 

heureka Aug 17, 2015

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