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Answer to Q90

Sally is 54 years old and her mother is 80, how many years ago was Sally's mother three times her age?

Let Sally's age be x
Let her mother's age be y

Now, x = 54 and y = 80
So, y - x = 26 (the mother will always be 26 years older than Sally at all time)

But there was a time when the mother's age was three times Sally's age.
So at that time: y = 3x - - eq i
But remember: y - x = 26 - - eq ii

From eq ii
y = 26 + x - - eq iii

Putting eq iii into eq i
26 + x = 3x
26 = 3x - x
26 = 2x
x = 26 ÷ 2
x = 13

So, when Sally was 13 her mother was 3 x 13 = 39. And to check, is 39 - 13, 26? Yes, so we are good.

But here is the tricky part, the question asked for how many years ago that scenario was not Sally's age at that time.

Sally is now 54 and the scenario was when she was 13, so that was 54 - 13 years ago

Answer: 41

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816 viewsedited  May 13, 2020 at 10:44

Answer to Q90

Sally is 54 years old and her mother is 80, how many years ago was Sally's mother three times her age?

Let Sally's age be x
Let her mother's age be y

Now, x = 54 and y = 80
So, y - x = 26 (the mother will always be 26 years older than Sally at all time)

But there was a time when the mother's age was three times Sally's age.
So at that time: y = 3x - - eq i
But remember: y - x = 26 - - eq ii

From eq ii
y = 26 + x - - eq iii

Putting eq iii into eq i
26 + x = 3x
26 = 3x - x
26 = 2x
x = 26 ÷ 2
x = 13

So, when Sally was 13 her mother was 3 x 13 = 39. And to check, is 39 - 13, 26? Yes, so we are good.

But here is the tricky part, the question asked for how many years ago that scenario was not Sally's age at that time.

Sally is now 54 and the scenario was when she was 13, so that was 54 - 13 years ago

Answer: 41

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