Age problems

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

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

c) Jessica is four years younger than Jennifer now. In 10 years, Jessica will be twice the age that Jennifer is now. 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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