Video: Pack 1 • Paper 1 • Question 14

Pack 1 • Paper 1 • Question 14

02:56

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.

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