From the information given,
One batch of pink paint is made from 2 cups of red paint and 7 cups of white paint.
This means that the ratio of red paint to white paint in 1 batch of pink paint is 2:7
By reducing to the lowest term, it becomes 1:3.5
This means that 1.5 cups of red paint is used with 3.5 cups of white paint.
This ratio is constant.
Let x represent the number of cups of white paint used. Given that he made a large amount of pink paint by using 14 cups of red paint, it means that the number of cups of white would be
1/3.5 = 14/x
By cross multiplying, it becomes
x = 3.5 * 14
x = 49 cups
49 cups of white paint would be used with 14 cups of red paint
3.5 cups of white paint is used per cup of red paint