Direct variation

Question

A recipe for 2 dozen corn muffins calls for 3 cups of flour. The number of muffins varies directly with the amount of flour you use. How many cups of flour would you need for 6 and a half dozen muffins?

Answer 1

2 dozen =2(12) = 24

6 1/2 dozen =6.5(12) = 78

3/2(12) = F/6.5(12) where F= cups of flower needed for 6 1/2 dozen Muffins

F = 3(6.5)(12)/24 = 19.5/2 = 9.75

= 9 3/4 cups of flour for 6 1/2 dozen

9.75/78= 3/24 = 1/8

there are 8 times as many corn Muffins as cups of Flour

the ratio of muffins to cups is a constant

M=8F

where M= number of Muffins, and F=number of ups of Flour

F=M/8

F= 6.5(12)/8 = 6.5(3)/2 = 19.5/2 = 9.75 = 9 3/4 cups of Flour