I need help on how to work the problem below. The teacher said the answer is 11, but I don't understand how you get there.
"The Big Screamer Coaster carries 92 people altogether. Some if its cars carry 4 passengers,and the rest carry 6 passengers. There are 3 less 6 passenger cars than 4 passenger cars. How many 4 passenger cars are there?"
Thanks...
number of 4 passenger cars --- x
number of 6 passenger cars --- y
assuming the coaster is filled to capacity ...
4x + 6y = 92 or 2x + 3y = 46
but y = x - 3
sub into first equation ....
2x + 3y = 46
2x + 3(x-3) = 46
2x + 3x - 9 = 46
5x = 55
x = 11
if x = 11, then y = x-3 = 8
there are 11 four passenger cars and 8 six passenger cars
check:
4(11) + 6(8) = 92
and 8 is 3 less than 11
To solve this problem, we need to break it down into steps.
Step 1: Define the variables.
Let's define a variable for the number of 4-passenger cars. Let's call it "x". We also know that there are 3 less 6-passenger cars, so we can define the number of 6-passenger cars as "x - 3".
Step 2: Translate the given information into equations.
We are told that the total number of cars is 92. Since some cars carry 4 passengers and the rest carry 6 passengers, we can write an equation for this:
4x + 6(x - 3) = 92.
Step 3: Solve the equation.
We can now solve the equation for x. Start by simplifying the equation:
4x + 6x - 18 = 92.
Combine like terms:
10x - 18 = 92.
Add 18 to both sides:
10x = 110.
Divide both sides by 10:
x = 11.
Step 4: Answer the question.
To answer the question "How many 4-passenger cars are there?", we substitute x = 11 into our initial definition of x:
There are 11 4-passenger cars.