USING LINEAR
EQUATIONS IN REAL LIFE
Omar Younis AL Shawabkeh
Grade 9 –B1
Math Project
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Introduction
• Students often wonder if, when, and how they will ever use math in "real
life" situations. The truth is that we use math all the time! The
underlying skills developed in math classrooms resonate throughout a
student's lifetime and often resurface to help solve various real-world or
work-related problems.
• Ask any contractor or construction worker--they'll tell you just how
important math is when it comes to building anything.
• Grocery shopping requires a broad range of math knowledge from
multiplication to estimation and percentages. Each time you calculate the
price per unit, weigh produce, figure percentage discounts, and estimate
the final price, you're using math in your shopping experience.
• You use math when convert from
Celsius to Fahrenheit to know the
temperature.
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What is Linear Equations?
Linear equations use
one or more variables
where one variable is
dependent on the other.
Almost any situation
where there is an
unknown quantity can
be represented by a
linear equation,
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How Linear Equations used in Real Life?
Linear equations are used in real life for example to
figure out income over time, calculating mileage
rates, or predicting profit. Many people use linear
equations every day, even if they do the calculations
in their head without drawing a line graph.
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How Linear Equations used in Real Life?
In Calculating Rates:
Linear equations can be a useful tool for comparing rates of pay. For
example, if one company offers to pay you $350 per week and the
other offers $8 per hour, and both ask you to work 20 hours per
week, which company is offering the better rate of pay? A linear
equation can help you figure it out! The first company's offer is
expressed as 350 = 20x. The second company's offer is expressed as y
= 8(20) = 160$. After comparing the two offers, the equations tell you
that the first company is offering the better rate of pay at $17. 5 per
hour.
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How Linear Equations used in Real Life?
In Budgeting
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. If the cost of the rental space is $780 and
the price per person for food is $9.75, a linear equation can be
constructed to show the total cost, expressed as y, for any number of
people in attendance, or x. The linear equation would be written as y
= 9.75x + 780. 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.
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How Linear Equations used in Real Life?
In Budgeting
Imagine that you are taking a taxi while on vacation. You know that the
taxi service charges $9 to pick your family up from your hotel and another
$0.15 per mile for the trip. Without knowing how many miles it will be to
each destination, you can set up a linear equation that can be used to
find the cost of any taxi trip you take on your trip. By using "x" to
represent the number of miles to your destination and "y" to represent the
cost of that taxi ride, the linear equation would be y = 0.15x + 9.
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System of Linear Equations in Real Life
This can help us solve many real-world problems. E.g. if you might be considering
two different phone contracts. The following is representing a real-life situation
where system of linear equations is used.
John is trying to choose between two phone plans. The first plan, with Vodafone,
costs $20 per month, with calls costing an additional 25 cents per minute. The
second company, Sellnet, charges $40 per month, but calls cost only 8 cents per
minute. Which should he choose?
John’s choice will depend upon how many minutes of calls he expects to use each
month. This needing writing two equations for the cost in dollars in terms of the
minutes used. Since the number of minutes is the independent variable, it will be
Cost
(x). is dependent on minutes - the cost per month is the dependent variable and will be
assigned y.
•For Vendafone: y = 0.25x + 20
•For Sellnet: y = 0.08x + 40
By writing the equations in slope-intercept form (y = mx + b), you can sketch a graph to
visualize the
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situation:
System of Linear Equations in Real Life
Cost is dependent on minutes - the cost per month is the dependent
variable and will be assigned y.
•For Vendafone: y = 0.25x + 20
•For Sellnet: y = 0.08x + 40
By writing the equations in slope-intercept form (y = mx + b), you can
sketch a graph to visualize the
situation:
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System of Linear Equations in Real Life
The line for Vendafone has an intercept of 20 and
a slope of 0.25. The Sellnet line has an intercept of
40 and a slope of 0.08 (which is roughly a third of
the Vendafone line's slope). In order to help John
decide which to choose, we'll find where the two
lines cross, by solving the two equations as a
system.
Since equation 1 gives us an expression for
y(0.25x + 20), we can substitute this expression
directly into equation 2:
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System of Linear Equations in Real Life
So if John uses 117.65 minutes a month (although he can't really do
exactly that, because phone plans only count whole numbers of
minutes), the phone plans will cost the same. Now we need to look
at the graph to see which plan is better if he uses more minutes
than that, and which plan is better if she uses
fewer. You can see that the Vendafone plan costs more when he uses
more minutes, and the Sellnet plan costs more with fewer minutes.
So, if John will use 117 minutes or less every month, he should
choose Vendafone. If he plans on using 118 or more minutes, he
should choose Sellnet.
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Conclusion
Math is very important in our lives. And there are many
real situations we face where we need to use system of
linear equations to take decision even if we didn’t realize
this.
Keep attention in your math class and gain the
knowledge you need for your future.
Thank You
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