Three Linear Variables

23 yellow, 30 pink and 12 blue balls

Step-by-step explanation:

Let the number of yellow, pink, blue, and black balls be y, p, b, and x respectively.

From 1st sentence:

y +p +b +x= 90

"60 of them are not pink"

➜ y +b +x= 60

Given that 25 are black, x= 25.

"67 of them are not yellow"

➜ p +b +x= 67

Subst. x= 25 into the above equations:

y +p +b +25= 90

y+ p +b= 65 (1)

y +b +25= 60

y +b= 35 (2)

p +b +25= 67

p +b= 42 (3)

I will rewrite the 3 equations for better clarity:

y +p +b= 65 (1)

y +b= 35 (2)

p +b= 42 (3)

(1) -(2):

p= 65 -35

p= 30

(1) -(3):

y= 65 -42

y= 23

Substitute p= 30 and y= 23 into (1):

23 +30 +b= 65

b= 65 -53

b= 12

Thus, there 23, 30 and 12 yellow, pink and blue balls respectively.