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Answered

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3. Four years ago, Jane was twice as old as Sam. Four years on from now, Sam will be 3/4 of Jane's
age. How old is Jane now?​

D3 Four Years Ago Jane Was Twice As Old As Sam Four Years On From Now Sam Will Be 34 Of Janesage How Old Is Jane Now class=

Sagot :

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Let

J = present age of Jane

S = present age of Sam

see table below,

[tex]\begin{bmatrix}&Name &Past &Present &Future\\&Jane &J-4 &J &J+4\\&Sam &S-4 &S &S+4\end{bmatrix}[/tex]

Conditions:

#1. Four years ago, Jane was twice as old as Sam

so we can say that 4 years ago J = 2S.

Now refer to table above. To get the correct equation, we should also consider their age 4 years ago. So the correct equation is now,

J - 4 = 2(S - 4)

#2. Four years on from now, Sam will be 3/4 of Jane's

so we can say that 4 years from now, S = ¾J

Now refer to table above again. To get the correct equation, we should also consider their age 4 years from now. So the correct equation is now,

S + 4 = ¾(J + 4)

Now we have 2 unknowns and 2 equations. So we can solve the missing variables.

J - 4 = 2(S - 4)

J - 4 = 2S - 8

J = 2S - 8 + 4

J = 2S - 4

substitute J in the 2nd equation,

S + 4 = ¾(J + 4)

S + 4 = ¾(J + 4)

S + 4 = ¾(2S - 4 + 4)

S + 4 = 6S/4

S + 4 = 3S/2

2S + 8 = 3S

S = 8

J = 2S - 4

J = 2(8) - 4

J = 16 - 4

J = 12

So the present age of Jane is 12 years old and present age of Sam is 8 years old.

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