Roger mixed 5/8 cup of red paint with 2/5 cup of yellow paint. how much red paint is needed (using the same ratio) if he wants to use 1 cup yellow paint

Set up the ratio as fractions

(5/8) cup red / (2/5) cup yellow = r amount of red / 1 cup yellow

Then cross multiply the numbers and set up as a equation like this

(5/8) × 1 = (2/5) × r

(5/8) = (2/5)r

Multiply both sides of the equation by (5/2) to get rid of the fraction and solve for r

(5/2) × (5/8) = (2/5)r × (5/2)

25/16 = r

Reduce down to 5/4 or change to a mixed number

1 and 1/4  cups = r