Question

The ratio of sandwiches with white bread to brown bread is 10:3. Out of the sandwiches that are white, 2 3 are vegetarian. Out of the sandwiches that are on brown bread, half are vegetarian. Wha

Answer 1

Ratio of sandwiches with white bread and brown bread is 10:3. Of the white sandwiches 2/3 are vegetarian, of the sandwiches that are brown half are vegetarian. What fraction of the sandwiches are vegetarian?

Explanation:

Givens

The ratio between white bread and brown bread is 10:3, that is, for every 10 white bread, there are 3 brown bread.

2/3 of white sandwiches are vegetarian.

1/2 of brown sandwiches are vegetarian.

We know that white bread is represented by 10, and brown bread is represents by 3. So, 2/3 of 10 are vegetarians, and 1/2 of 3 are vegetarians. The sum of them is

2/3 of 10 are vegetarians =
`(2)/(3) * 10 = (20)/(3)`

1/2 of 3 are vegetarians =
`(1)/(2) * 3 = (3)/(2)`

`=(20)/(3)+(3)/(2)\\\\=(40+9)/(6)\\\\=(49)/(6)`

Therefore, 49/6 represents all the sandwiches which are vegetarian.