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??

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