A teacher wrote a system of equations involving the number of girls, g, and the number of boys, b, in her classroom. Solve the system and state if the solution is reasonable.
2g plus b equals 59 line break b equals 100 minus 4g
b = 18, g = 20.5; the solution is reasonable
b = 18, g = 20.5; the solution is not reasonable
b equals negative 6, g = 26.5; the solution is not reasonable
b = 6, g = 26.5; the solution is reasonable
To solve the system of equations, we can substitute the value of b from the second equation into the first equation:
2g + (100 - 4g) = 59
2g + 100 - 4g = 59
-2g + 100 = 59
-2g = -41
g = 20.5
Then, we can substitute this value back into the second equation to solve for b:
b = 100 - 4(20.5)
b = 100 - 82
b = 18
Therefore, the correct solution is b = 18, g = 20.5. This solution is reasonable as it satisfies both equations in the system. The number of boys is 18 and the number of girls is 20.5, which makes sense in the context of a classroom.
the answer was b not a
Apologies for the confusion. Let's reevaluate the solution:
Given equations:
1) 2g + b = 59
2) b = 100 - 4g
Substitute equation 2 into equation 1:
2g + (100 - 4g) = 59
2g + 100 - 4g = 59
-2g + 100 = 59
-2g = -41
g = 20.5
Substitute g = 20.5 into equation 2 to find b:
b = 100 - 4(20.5)
b = 100 - 82
b = 18
Therefore, the correct solution is b = 18, g = 20.5. This solution is reasonable as it satisfies both equations in the system. The number of boys is 18, and the number of girls is 20.5, making sense in the context of a classroom.