1) a mixed school can accomadate a maximum of 440 students the number of girls must be at least 120 while the number of boys must exceed 150 taking x to represent the number of boys and y the number of girls write down the number all the inequalities representing the information above
2)the sum of three consecutive odd integers is greater than 219 determine the first three such integers
1) x + y ≤ 440 (maximum capacity)
y ≥ 120 (at least 120 girls)
x > 150 (more than 150 boys)
2) Let the first odd integer be n. Then the next two consecutive odd integers are n+2 and n+4.
The sum of these three integers is:
n + (n+2) + (n+4) = 3n + 6
According to the problem, this sum is greater than 219:
3n + 6 > 219
Subtracting 6 from both sides:
3n > 213
Dividing by 3:
n > 71
Therefore, the first odd integer must be greater than 71. The first three consecutive odd integers greater than 71 are:
73, 75, 77