A shipping company charges the shipping cost of $10 per kg for packages weighing equal to 5 kg. For packages weighing more than 5 kg but less than 11 kg, the shipping cost is $8 per kg. On a certain day, the company shipped a total of 140 packages and earned $8760. The total weight of the packages was 1020 kg. Maximum how many packages could weigh 6 kg? (Assume all packages have integral weight of more than or equal to 5 kg.)1) 602) 323) 244) 20
Question
A shipping company charges the shipping cost of 8 per kg. On a certain day, the company shipped a total of 140 packages and earned $8760. The total weight of the packages was 1020 kg. Maximum how many packages could weigh 6 kg? (Assume all packages have integral weight of more than or equal to 5 kg.)1) 602) 323) 244) 20
Solution
To solve this problem, we first need to understand the cost structure. The company charges 8 per kg for packages weighing more than 5 kg but less than 11 kg.
Given that the total weight of the packages was 1020 kg and the company earned $8760, we can set up the following equation to represent the total cost:
10x + 8y = 8760
where x is the number of 5 kg packages and y is the number of packages weighing more than 5 kg but less than 11 kg.
We also know that the total number of packages is 140, so we can set up another equation:
x + y = 140
We also know that the total weight of the packages is 1020 kg, so we can set up a third equation:
5x + 6y = 1020
We now have a system of three equations, which we can solve simultaneously to find the values of x and y.
First, we can subtract the second equation from the third to get:
y = 1020 - 5x
Substituting this into the first equation gives:
10x + 8(1020 - 5x) = 8760
Solving this equation for x gives:
x = 60
Substituting x = 60 into the second equation gives:
y = 140 - 60 = 80
So, the maximum number of packages that could weigh 6 kg is 80. Therefore, the answer is not in the options provided.
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