Age problems

A) Alex is three times as old as he was two years ago. How old is he now?

b) Three years ago, Casey was twice as old as his sister. Now, he is five years older. How old is Casey?

c) Jessica is four years younger than Jennifer now. In 10 years, Jessica will be twice that of Jennifer. Find the present ages of Jennifer and Jessica,

Correct answer:

A =  3
C =  16
J =  2

Step-by-step explanation:

$$\begin{gathered} A=3(A-2) \\ A=3\cdot (A-2) \\ 2A=6 \\ A=\frac{6}{2}=3 \\ A=3 \end{gathered}$$

$$\begin{gathered} C=2(S-3) \\ C=S+5 \\ C=2\cdot (S-3) \\ C=S+5 \\ C-2S=-6 \\ C-S=5 \\ Row2-Row1\to Row2 \\ C-2S=-6 \\ S=11 \\ S=\frac{11}{1}=11 \\ C=-6+2S=-6+2\cdot 11=16 \\ C=16 \\ S=11 \end{gathered}$$

$$\begin{gathered} J=N-4 \\ J+10=2\cdot N \\ J-N=-4 \\ J-2N=-10 \\ Row2-Row1\to Row2 \\ J-N=-4 \\ -N=-6 \\ N=\frac{-6}{-1}=6 \\ J=-4+N=-4+6=2 \\ J=2 \\ N=6 \end{gathered}$$

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