Answer:
- Red beans =36
- Green beans = 12
- Yellow beans = 12
- Orange beans =6
- Black beans = 6
Step-by-step explanation:
If we assume that "x" is the total number of beans:
- Red beans: x/2
- Green beans: 1/6 (x) = x/6
- Yellow beans: 1/6 (x) = x/6
- Orange beans: 1/12 (x) = x/12
- Black beans = 6
So, the sum of all the beans:
x/2 + x/6 +x/6 +x/12 +6 =x
Multiplying each term by 12:
(12) x/2 + (12)x/6 + (12)x/6 + (12)x/12 + (12)6 = (12)x
6x +2x+2x+x+72=12x
Isolating "x":
72 =12x -6x-2x-2x-x
72=x
Replacing the value of x in each equation of each bean:
- Red beans: x/2: 72/2 =36
- Green beans: 1/6 (x) = x/6= 72/6 = 12
- Yellow beans: 1/6 (x) = x/6=72/6 = 12
- Orange beans: 1/12 (x) = x/12 = 72/12=6
- Black beans = 6
