Ann is 12 years old. Her mother is 3 times as old as Ann. How many years ago was her mother 4 times as old as Ann?

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Answer 1 · 2018-05-11T04:54:27

4 years ago

If we call Ann´s age A and mother´s age M:

$A = 12$ $A = 12$

$A \cdot 3 = M$ $A * 3 = M$

, a few years back ( Y ):

$(A - Y) \cdot 4 = (M - Y)$ $( A - Y ) * 4 = ( M - Y )$

So, by substitution:

$(A - Y) \cdot 4 = (A \cdot 3 - Y)$ $( A - Y ) * 4 = ( A * 3 - Y )$

$4 A - 4 Y = 3 A - Y$ $4A - 4Y = 3A - Y$

$4 A - 3 A = 4 Y - Y$ $4A - 3A = 4Y - Y$

$A = 3 Y$ $A = 3Y$

$Y = \frac{A}{3} = \frac{12}{3} = 4$ $Y = A/3 = 12/3= 4$

Answer 2 · 2018-05-11T08:30:15

$4$ $4$ years ago.

We know both of their present ages.

If Ann is $12$ $12$ years old, then her mother is $3 \times 12 = 36$ $3xx 12=36$ years old.

A number of years ago,they were both younger.
Let the number of years be $x$ $x$ .

Ann's age was $12 - x$ $12-x$ and her mother's age was $36 - x$ $36-x$

$36 - x = 4 (12 - x) \leftarrow$ $36-x =4(12-x)" "larr$ the mom was $4$ $4$ times older,

$36 - x = 48 - 4 x$ $36-x = 48-4x$

$4 x - x = 48 - 36$ $4x-x = 48-36$

$3 x = 12$ $3x = 12$

$x = 4$ $x=4$

It was $4$ $4$ years ago.

Check: Ann was $8$ $8$ and her mom was $32$ $32$

$4 \times 8 = 32$ $4 xx8 = 32$