Fifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment. Which equation can be used to solve for x, the total amount of paint in the mixture of the two colors?
Answers
% of black pigment in A = 15
% of black pigment in B = 60
let total amount of paint = x ml
so amount of back pigment in x ml = 25% of x = x/4 ml
given that amount of paint A = 40 ml
so remaining Paint B = total paint - 40 = (x - 40)ml
Quantity of black pigment in A = 15% of 40 ml = (15/100) × 40 = 6 ml
Quantity of black pigment in B = 60% of (x -40 ) = (60/100) × (x - 40)
= 3/5( x - 40 ) = 3x/5 - 24
Quantity of black pigment in resulting mixture = 25% of x = x/4
Quantity of black pigment in resulting mixture = Quantity of black pigment in A +
Quantity of black pigment in B
⇒ x/4 = 6 + (3x/5 - 24)
⇒ x = 4 ( 3x/5 - 18)
⇒ 5x = 4 ( 3x - 90 )
⇒ 5x = 12x - 360
⇒ 12x -5x = 360
⇒ 7x = 360
so 7x - 360 = 0 is the equation , which if solved for x will give total amount of paint
⇒ x = 360/7 = 51.4285 ml
total amount of paint = 51.4285 ml or 360/7 ml
Answer:
0.15(40) + 0.6(x – 40) = 0.25(x)
Step-by-step explanation: