Andy cut a tuna sandwich and a chicken sandwich into a total of 15 same size pieces. He cut the tuna sandwich into 9 more pieces than the chicken sandwich. Andy ate 8 pieces of the tuna sandwich. What fraction of the tuna sandwich did he eat?
To find the fraction of the tuna sandwich that Andy ate, we need to know the total number of pieces the tuna sandwich was cut into.
Let's assume the number of pieces Andy cut the chicken sandwich into is x.
According to the given information, Andy cut the tuna sandwich into 9 more pieces than the chicken sandwich. So, the number of pieces he cut the tuna sandwich into will be x + 9.
The total number of pieces for both sandwiches is given as 15. Therefore, the equation can be set up as follows: x + (x + 9) = 15.
Simplifying the equation, we have: 2x + 9 = 15.
Subtracting 9 from both sides, we get: 2x = 6.
Dividing both sides by 2, we find: x = 3.
So, Andy cut the chicken sandwich into 3 pieces, and therefore, he cut the tuna sandwich into 3 + 9 = 12 pieces.
Since Andy ate 8 pieces of the tuna sandwich, the fraction of the tuna sandwich that he ate is 8/12.
Simplifying the fraction, we have: 8/12 = 2/3.
Therefore, Andy ate 2/3 of the tuna sandwich.