Question 952520
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20 years ago Grandma was twice as old as Mum. Today, Grandma is twice the age Mum was when I was born. How old am I?
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Let Grandma's current age, be G, and Mum's, M
Then 20 years ago Grandma was G - 20, and Mum was M - 20
Given that, "20 years ago Grandma was twice as old as Mum," gives us:
G - 20 = 2(M - 20) ===> G - 20 = 2M - 40 ===> G = 2M - 40 + 20 ===> G = 2M - 20 ---- eq (i)
G - 20 = 2(M - 20) ===> G - 20 = 2M - 40____G - 20 + 40 = 2M ===> G + 20 = 2M ====> {{{(G + 20)/2 = M}}} ----- eq (ii)
Let the number of years since my birth, be y
Mum's age, when I ws born: M - y, or {{{(G + 20)/2 - y}}}
"Today, Grandma is twice the age Mum was when I was born," gives us: G = 2(M - y)
                                                                                                                            {{{G = 2((G + 20)/2 - y)}}} ----- Substituting {{{(G + 20)/2}}} for M
                                                                                                                            G = G + 20 - 2y
                                                                                                              G - G - 20 = - 2y ---- Subtracting 20 from each side
                                                                                                                        - 20 = - 2y
                                                                <font color  = red>Years since I was born/my age</font>, or {{{y = (- 20)/(- 2) = highlight(10)}}}</font></font></font></b></pre>