Application of linear equations in real life

Linear equations can be a useful tool for comparing rates of pay. A linear equation can help you figure it out! A party planner has a limited budget for an upcoming event. She'll need to figure out how much it will cost her client to rent a space and pay per person for meals.

With this equation, the party planner can substitute any number of party guests and give her client the actual cost of the event with the food and rental costs included. One of the most helpful ways to apply linear equations in everyday life is to make predictions about what will happen in the future. While real world factors certainly impact how accurate predictions are, they can be a good indication of what to expect in the future.


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Linear equations are a tool that make this possible. With hands-on experience in the traditional classroom, the online setting, and the world of curriculum development, Jessica Smith is a veteran educator who is passionate about learning. Smith earned a M. How to Figure the Percentage of Change.

Setting up a Linear Equation to Solve a Real-World Application

How to Calculate Average Increase. By Jessica Smith; Updated March 13, Sciencing Video Vault. References Math Warehouse: So, it looks like it will take the two machines, working together, 1.

Linear Equations in the real world

The basic word equation for this problem is,. This time we know that the time spent working together is 3. We now need to find the work rates for each person. We are going to be looking at mixing solutions of different percentages to get a new percentage. The solution will consist of a secondary liquid mixed in with water. The secondary liquid can be alcohol or acid for instance.

Note as well that the percentage needs to be a decimal. However, this is exactly what we want. The basic equation tells us to look at how much of the secondary liquid is in the water. So, this is the correct wording.

Melting Snow

So, the new word equation is,. Do not get excited about the zero in the first term. This is okay and will not be a problem. So, we need to add in Notes Quick Nav Download. Notes Practice Problems Assignment Problems. You appear to be on a device with a "narrow" screen width i. Due to the nature of the mathematics on this site it is best views in landscape mode.

If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. Okay, this may be a little bit of overkill here. However, the point of these first two steps is that you must read the problem. You need to read the problem very carefully and as many times as it takes.

In the Kitchen

You are only done with this step when you have completely understood what the problem is asking you to do. This includes identifying all the given information and identifying what you are being asked to find. Sometimes a single word can completely change how the problem is worked. If you just skim the problem you may well miss that very important word. Represent one of the unknown quantities with a variable and try to relate all the other unknown quantities if there are any of course to this variable.

If applicable, sketch a figure illustrating the situation. This may seem like a silly step, but it can be incredibly helpful with the next step on occasion. Form an equation that will relate known quantities to the unknown quantities. To do this make use of known formulas and often the figure sketched in the previous step can be used to determine the equation. Solve the equation formed in the previous step and write down the answer to all the questions.

It is important to answer all the questions that you were asked. Often you will be asked for several quantities in the answer and the equation will only give one of them. Check your answer. Do this by plugging into the equation, but also use intuition to make sure that the answer makes sense. Example 1 In a certain Algebra class there is a total of possible points. These points come from 5 homework sets that are worth 10 points each and 3 hour exams that are worth points each.

A student has received homework scores of 4, 8, 7, 7, and 9 and the first two exam scores are 78 and Assuming that grades are assigned according to the standard scale and there are no weights assigned to any of the grades is it possible for the student to receive an A in the class and if so what is the minimum score on the third exam that will give an A?

What about a B?

Example 2 We want to build a set of shelves. The width of the set of shelves needs to be 4 times the height of the set of shelves and the set of shelves must have three shelves in it. If there are 72 feet of wood to use to build the set of shelves what should the dimensions of the set of shelves be?

Algebra 25 - Linear Equations in the Real World

How much did the store pay the manufacturer of the calculator? How much was the shirt being sold for before the sale? Show Solution This problem is pretty much the opposite of the previous example. Example 5 Two cars are miles apart and moving directly towards each other. One car is moving at a speed of mph and the other is moving at 70 mph.

Linear Equations in the Real World. See linear equations in our everyday lives.

Assuming that the cars start moving at the same time how long does it take for the two cars to meet? Example 6 Repeat the previous example except this time assume that the faster car will start 1 hour after slower car starts. Show Solution For this problem we are going to need to be careful with the time traveled by each car. Here is the equation and solution for this example.

Example 7 Two boats start out miles apart and start moving to the right at the same time. The boat on the left is moving at twice the speed as the boat on the right. Five hours after starting the boat on the left catches up with the boat on the right.


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