Answer: There are 3615 buttons
Step-by-step explanation:
From this situation we can write a system of equations if we tag the orange buttons with , the yellow buttons with
, the green buttons with
and the blue buttons with
:
There were 820 orange buttons:
(1) Number of orange buttons
The number of orange buttons was 160 fewer than the number of yellow buttons:
(2)
The number of orange buttons was 210 more than the number of green buttons:
(3)
1/3 of the total number of buttons in the container were blue buttons:
If the total is the sum of the buttons of each color, we have:
(4)
At this point we have our system with 4 equations and 4 unknowns.
Let's begin by substituting (1) in (2):
(5)
Isolating :
(6) Number of yellow buttons
Subsituting (1) in (3):
(7)
Isolating :
(8) Number of green buttons
Substituting (1), (6) and (8) in (4):
(9)
Isolating :
(10) Number of blue buttons
Now we can find the total number of buttons:
(11) This is the total number of buttons