last year my sister was 7/8 the age of my brother, how old is my sister?
age difference a year ago is b= s+1/8 age ratio s = 7/8 b
therefore s = 7/8 (s+1/8)
is this correct logic?
let brothers age last year be x
then sister's age last year = 7x/8
brother's age now = x+1
sister's age now = 7x/8 + 1 = (7x+8)/8
we need one more piece of information to actually find the age.
e.g. if brother last year was 8
then sister last year was 7
now brother is 9 and sister is 8
if brother last year was 16
then sister last year was (7/8)(16) = 14
brother now is 17 and sister is 15
etc.
Your logic is partially correct, but there is a small mistake in your equation. Let me explain in more detail.
Let's say the age of your sister last year was 's' and the age of your brother last year was 'b'. You correctly stated that the age difference a year ago was 'b = s + 1/8'. This means that your brother's age last year is equal to your sister's age last year plus 1/8.
To find your sister's age, you can set up a ratio using the age difference. You correctly stated the ratio as 's = 7/8 b'. This means that your sister's age last year was 7/8 times your brother's age last year.
However, the mistake you made is in the equation 's = 7/8 (s + 1/8)'. The parentheses indicate the order of operations, and multiplying '7/8' only applies to 's'. To correct it, you should distribute the '7/8' to both 's' and '1/8'. The correct equation should be:
s = 7/8s + 7/64
To solve this equation, you can subtract '7/8s' from both sides of the equation:
s - 7/8s = 7/64
Simplifying this equation, you get:
1/8s = 7/64
To isolate 's', you can multiply both sides of the equation by '8/1':
(1/8s) * (8/1) = (7/64) * (8/1)
s = 7/8
So, according to your given information and calculations, your sister was 7/8 years old last year.