Final answer:
The system of equations to determine the number of each flavor of gummy bears is comprised of: total gummy bears (O + G + S = 38), the grape to orange relationship (G = 2O - 6), and the strawberry to grape relationship (S = G/2). These can be solved sequentially to find the quantity of each flavor.
Step-by-step explanation:
To determine the number of each flavor of gummy bears in the bag given the conditions, we can set up the following system of equations: Let's denote the number of orange gummy bears as O, the number of grape gummy bears as G, and the number of strawberry gummy bears as S. According to the problem, there are 6 fewer than twice as many grape gummy bears as orange ones, so we have the equation G = 2O - 6. It is also stated that there are half as many strawberry gummy bears as there are grape gummy bears, giving us the equation S = G/2. Furthermore, since the bag contains 38 gummy bears in total, we have the equation O + G + S = 38. Thus, our system of equations is:
- O + G + S = 38 (Total number of gummy bears)
- G = 2O - 6 (Grape is twice orange minus 6)
- S = G/2 (Strawberry is half of grape)
To solve this system, we can substitute the expressions for G and S from the second and third equations into the first equation and solve for O. Once we find O, we can use it to find G and S.