Explain in your own words what it means for an equation to model a real world situation an give an example.
-it is right to say that when given a problem, we want to identify the quality of the problem we want to find, translate form word to algebra, and make up an equation base on given and solve for it. For example, LxWxH to determine how much space can take up.
I am on a limited budget for a long weekend to Maine. I have $100 and I have budgeted 40% for gas. My car is on empty and it gets 20 MPG. The average price of gas is $3.00 per gallon and the round trip to Maine is 300 miles. Do I have enough in my budget for Maine or am I going to have to change my plans and go to New Hampshire?
b=budget g=gas for roundtrip
c=cost of gas for roundtrip
c=g x 3.00
equation is c < b
yes=going to Maine
no=not going to Maine
What is my budget for gas?
b = budget
b = 100 x .40 b = 40
How many gallons of gas will I use roundtrip?
g = gas
g = 300/20 g = 15
What is the total cost for gas?
c = cost
c = 15 x 3.00 c = 45.00
Is c < 40.00
Looks like I am not going to Maine
first do 40% off 100
it is 45.00
Well, you know what they say, equations and real world situations go together like peanut butter and jelly sandwiches. When we say an equation models a real world situation, it simply means that the equation represents the relationships or patterns that exist in the real world problem we're trying to solve. It's like using a mathematical language to understand the world around us.
For example, let's say you're trying to figure out how much popcorn you can fit in a cylindrical container. You know that the space popcorn takes up can be determined by its length (L), width (W), and height (H). So, you create the equation LxWxH.
Now, when you plug in the actual values for L, W, and H, you can solve the equation to determine the exact amount of space the popcorn will occupy. In this case, the equation becomes just as important as the popcorn itself. It's like solving a deliciously crunchy puzzle!
When we say that an equation models a real world situation, it means that the equation represents a relationship between variables that can help us understand and solve a problem related to the real world. It allows us to quantify and analyze the situation mathematically.
For example, let's say we are given a problem where we need to determine the amount of space a rectangular box can take up. In this scenario, we can use the equation LxWxH (Length times Width times Height) to represent the volume of the box. The variables L, W, and H represent the dimensions of the box, and by multiplying them, we obtain the total volume of the box. This equation models the real world situation of measuring the space occupied by a rectangular box.
By utilizing this equation, we can determine the volume of the box based on the given dimensions and solve the problem at hand. This approach allows us to translate the words of the problem into algebraic language and use the equation to find a numerical solution.