A cable car has 𝑛 passengers. Assuming that each passenger weighs 197 pounds, the weight of the car is 790 pounds, and the maximum load the cable can carry without breaking is 1980 pounds. What is the maximum value of 𝑛 that will keep the weight of the load beneath the maximum?
We have a cable car. The cable that holds the car can hold 1980 pounds before it breaks. To ensure the safety of the passengers, we need to make sure we know how many passengers can ride this cable car if they all weigh 197 pounds. When the car is empty, it weighs 790 pounds. And so the total weight of the cable car will be 790 pounds plus the passengers weight. This value needs to be less than 1980. But how do we calculate the passengers weight? Each passenger weighs 197 pounds. And there are 𝑛 passengers. The total passengers weight is then equal to each person’s weight times the number of people on board, 197 times 𝑛. We can write it like this, 197𝑛.
And now our job is to find out the number 𝑛 that makes this statement true. To do that, we get 𝑛 by itself. First, we subtract 790 pounds from both sides of our inequality. On the left, we’ll have 197𝑛 and, on the right, we will have 1190. From there, we can divide both sides of the equation by 197 pounds. 1190 divided by 197 is equal to 6.04060 continuing. But what does that mean in context to this problem? We know that six people could ride. And the decimal value represents a part of a person. And since we wouldn’t send 0.0406 parts of a person, we need to round down to our nearest whole number.
And so we say that the maximum value 𝑛 could be is six. If all the people weigh 197 pounds, the maximum number of people this cable car could hold is six. If we wanted to check and make sure this was true. we could plug the number we found, six, back into the original equation we wrote. We want to know, is 790 plus 197 times six less than the breaking point 1980. When we do that, we get 1972 which is less than 1980 which confirms our answer of six.