Question 1206221
T = total
G = green
B = blue
P = pink


T = G + B + P
P = 84 so .....
T = G + B + 84
3/8 of the buttons are green, so .....
T = 3/8 * T + B + 84
there are 20 more blue buttons than green, so .....
T = 3/8 * T + 3/8 * T + 20 + 84
combine like terms to get:
T = 6/8 * T + 104
subtract 6/8 * T from both sides of the equation to get:
2/8 * T = 104
solve for T to get:
T = 104 * 8/2 = 416


since T = 416 and P = 84, then .....
416 = G + B + 84
subtract 84 from both sides of the equation to get:
332 = G + B
since G = 3/8 * T, then .....
G = 3/8 * 416 = 156
since B = G + 20, then .....
B = 176


you have:


T = 416
P = 84
G = 156
B = 176


since T = G + B + P, then .....
T = 156 + 176 + 84 = 416.


your solution is that there were 176 blue buttons.