a. By using the butterfly method, the value of x is equal to 8.
b. By using the butterfly method, the value of y is equal to 20/3.
In Mathematics and Geometry, a direct proportion refers to a mathematical equation which is typically used to represent the equality of two (2) ratios.
Part a
By applying direct proportion to the given information, we have the following mathematical equation:
2/5 = x/20
By using the butterfly method, we would cross-multiply as follows;
x × 5 = 20 × 2
5x = 40
x = 40/5
x = 8
Part b
2/3 = y/10
2 × 10 = 3 × y
20 = 3y
y = 20/3