想問2條中3數學題

1.
If 2 times the sum of two consecutive even numbers is greater than 94, what is thesmallest possible value of the larger number.

Solution :
Let n be the larger number.
Then, the smaller number = n - 2

The sum of the two numbers is greater than 94 :
2 * [n + (n - 2)] > 94
4n - 4 > 94
4n > 98
n > 24.5

Since n is an even number, then
the smallest possible value of the larger number = 26


2.
A company has two factories A and B. Factory A has 62 workers andfactory B has 40 workers. The manager of the company is going to employ a total of 39 more newworkers. The new workers will be appointed to the two factories in the way thatthe total number of workers in factory A is not more than twice the totalnumber of workers in factory B. How many new workers can be appointed tofactory A at most?

Solution :
Let n be the number of new workers appointed to factory A.
Then, the number of new workers appointed to factory B = 39 - n

62 + n ≤ 2[40 + (39 - n)
62 + n ≤ 158 - 2n
3n ≤ 96
n ≤ 32

Number of new workers can be appointed to factory at most = 32