### Video Transcript

Yan bought vegetarian and
nonvegetarian burgers and sausages for a barbecue. The ratio of burgers to sausages
was two to five. The ratio of nonvegetarian to
vegetarian burgers was four to three. The ratio of nonvegetarian to
vegetarian sausages was five to two. What fraction of the food was
vegetarian?

As the ratio of burgers to sausages
was two to five, two-sevenths of the food were burgers and five-seventh of the food
were sausages. Two plus five is equal to
seven. In terms of the burgers, the ratio
of nonvegetarian to vegetarian was four to three. This means that three-sevenths of
the burgers were vegetarian. The ratio of nonvegetarian to
vegetarian sausages was five to two. This means that two-sevenths of the
sausages were vegetarian.

As three-sevenths of the burgers
were vegetarian and two-sevenths of the food were burgers, we need to work out
three-sevenths of two-sevenths. This is the same as three-sevenths
multiplied by two-sevenths. In order to multiply fractions, we
multiply the numerators and we multiply the denominators. Three times two is equal to six and
seven times seven is equal to 49. Two-sevenths of the sausages were
vegetarian and five-sevenths of the food were sausages. We, therefore, need to work out
two-sevenths of five-sevenths. Once again, this is the same as
two-sevenths multiplied by five-sevenths. Two multiplied by five is 10 and
seven multiplied by seven is 49.

We can therefore say that six
forty-ninths of the food were vegetarian burgers and ten forty-ninths of the food
were vegetarian sausages. Adding these two fractions will
give us the total amount of food that was vegetarian: six forty-ninths plus ten
forty-ninths. As we already have a common
denominator, in this case 49, we just need to add the numerators: six plus 10 is
equal to 16.

This means that the fraction of
food that was vegetarian is sixteen forty-ninths or 16 out of 49.