. The number of drops of red tint needed to make a certain shade of purple paint varies directly with the number of gallons of paint base. Suppose that 5 drops of red tint can be mixed with 2 gallons of paint base to create the correct shade. How many drops of red tint must be mixed with 6 gallons of paint base to create the correct shade?

15 drops of red tint must be mixed with 6 gallons of paint base to create the correct shade

Step-by-step explanation:

The number of drops of red tint needed to make a certain shade of purple paint varies directly with the number of gallons of paint base.

This is expressed Mathematically as:

= R ∝ P

Where R = Red paint

P = Paint base

R = kP

Suppose that 5 drops of red tint can be mixed with 2 gallons of paint base to create the correct shade.

Hence

5 = 2k

k = 5/2

How many drops of red tint must be mixed with 6 gallons of paint base to create the correct shade?

This is calculated as:

R = kP

Where k = 5/2

Hence:

R = 5/2 × 6

R = 15 drops of red tint

Hence, 15 drops of red tint must be mixed with 6 gallons of paint base to create the correct shade.

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