Question 218792
If Rita is eight years old, is twice as old as her sister.  How old will Rita be when she is one and a four times as old as her sister?


Let the amount of years that it takes for Rita to be 1 1/4, or {{{5/4}}} times her sister's age be y


Since Rita is 8, and her sister's 4


We'll therefore have: {{{8 + y = (5/4)*(4 + y)}}}


{{{8 + y = (20 + 5y)/4}}}


32 + 4y = 20 + 5y ----- Cross-multiplying 


4y - 5y = 20 - 32


- y = - 12


y = {{{(-12)/-1}}} = 12 


Therefore, in 12 years' time, Rita will be {{{5/4}}} times her sister's age, which means that she will be {{{highlight_green(20)}}} (8 + 12) years-old.


This would also mean that in 12 years' time, her sister will be 16 (4 + 12).


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Check
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{{{8 + 12 = (5/4)*(4 + 12)}}}


{{{20 = (5/4)*16}}}


20  =  20 (TRUE)