1) Invested $3000 - part of it invested at 10 percent simple annual interest and part at 8 percent simple annual interest; $256 of interest after a year - how much invested at 10 percent and how much at 8 percent?
Alright, so a good place to start setting up equations is to carefully read the problem, and identify any variables we might need. Here, the unknowns are "how much invested at 10 percent?" and "how much [invested] at 8 percent?" So, let's let
x be the amount of money invested at 10 percent interest and
y be the amount of money invested at 8 percent. You're told the interest is simple annual, so that makes the calculations a lot easier. What expression can you create, in terms of
x, that stands for the interest gained from the money invested at 10 percent? What expression can you create, in terms of
y, that stands for the interest gained from the money invested at 8 percent? A careful reading of the problem tells us that these two expressions you just created must sum to 256. Now, you try finishing up from here.
2) two cars from same point straight course opposite directions for 2 hours at 208 miles apart; 1 car traveled on average 8 miles per hour faster than other car, what is average speed of both cars for 2 hour trip?
Reading the problem, we can see that we'll again need two variables. This time, let
x be the speed of the first car, and let
y be the speed of the second car. You're told that "one car traveled on average 8 miles per hour faster than other car." If we say that the first car is the faster car, what expression can you create to model this information? Now, we know each car drove for two hours, so you can create expressions to stand for the total distance they drove after 2 hours? Then the problem tells us that these two expressions sum to 208. Now, you try finishing up from here.
3) charter aircraft at fixed total cost. if 36 rather than 40 are charged, 36 get charged 12 dollars more pp. what is fixed cost to charter? what is cost pp if 40 charter plane?
I'm thinking this problem was translated from another language, as I'm finding it a bit difficult to follow. What I think it says is this:
To charter an airplane costs a fixed amount of money. The airplane can carry up to 40 passengers. If only 36 passengers charter the airplane, the cost per person is 12 dollars more than if 40 people had chartered it. What is the fixed cost of the airplane? What is the cost per person if 40 people had chartered it?
Assuming the above is correct, we'll need two variables. Let
c be the fixed cost of chartering the airplane, and
p be the cost per passenger. It stands to reason that each person would be an equal portion of the cost, so when the airplane is full, there would be 40 people each paying an equal share. What expression can you create, in terms of
p, to model this information? Now we're told that if only 36 people charter the airplane, the cost per passenger is 12 dollars more. What expression can you create, in terms of
p, to model "12 dollars more than?" We have 36 passengers paying this new amount, and 40 passengers paying the old amount, and we know that the cost must always be the same, so what equation can you create based on this information? Now, you try finishing up from here.
