maths problem ratio

Question

Sarah and Henry share some sweets in the ratio 7:6 . 

Sarah eats 24 of her sweets and the ratio of sweets left becomes 1:2 . 

How many sweets did Henry have?

Answer 1

If Sarah and Henry share sweets in a 7:6 ratio, that means for some value x, Sarah has 7x sweets and Henry has 6x sweets. We are also given that after Sarah eats 24 of her sweets, the ratio becomes 1:2. Once Sarah eats 24, she has 7x-24 sweets left, and this is supposed to be half of what Henry has, which is 6x. So

7x-24 = 1/2 (6x) ==> 7x-24 = 3x ==> 4x = 24 ==> x = 6

So Henry had 6x = 6(6) = 36 sweets.