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?

a) 0.15(40) + 0.6x = 0.25(40 + x)
b) 0.15(40) + 0.6(x – 40) = 0.25(x)
c) 0.15(40) + 0.6x = 0.25(40 – x)
d) 0.15(40) + 0.6(x + 40) = 0.25(x)

A)  

Step-by-step explanation:

Given : The proportion of pigment in paint color A is black = 0.15

The amount of paint color A= 40 ml

Then , amount of black pigments in paint color A =

Let the unknown amount of paint color B be x.

The proportion of pigment in paint color B is black = 0.6

Then , amount of black pigments in paint color B=

The proportion of pigment in mixture is black = 0.25

Total quantity of mixed color =

Then amount of black pigments in mixture =

Now, the  equation which can be used to solve for x, the total amount of paint in the mixture of the two colors is given by :-

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺