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Example Questions
Example Question #1 : Equations
Tom is painting a fence feet long. He starts at the West end of the fence and paints at a rate of
feet per hour. After
hours, Huck joins Tom and begins painting from the East end of the fence at a rate of
feet per hour. After
hours of the two boys painting at the same time, Tom leaves Huck to finish the job by himself.
If Huck completes painting the entire fence after Tom leaves, how many more hours will Huck work than Tom?
Tom paints for a total of hours (2 on his own, 2 with Huck's help). Since he paints at a rate of
feet per hour, use the formula
(or
)
to determine the total length of the fence Tom paints.
feet
Subtracting this from the total length of the fence feet gives the length of the fence Tom will NOT paint:
feet. If Huck finishes the job, he will paint that
feet of the fence. Using
, we can determine how long this will take Huck to do:
hours.
If Huck works hours and Tom works
hours, he works
more hours than Tom.
Example Question #1 : Setting Up Equations
If the roots of a function are , what does the function look like in
format?
No equation of this form is possible.
This is a FOIL problem. First, we must set up the problem in a form we can use to create the function. To do this we take the opposite sign of each of the numbers and place them in this format: .
Now we can FOIL.
First:
Outside:
Inside:
Last:
Then add them together to get .
Combine like terms to find the answer, which is .
Example Question #2 : Setting Up Equations
Two numbers have a ratio of 5:6 and half of their sum is 22. What are the numbers?
Set up the equation:
Solve the equation:
Find the two numbers:
The two numbers have a ratio of 5:6, therefore the ratio can also be represented as:
The two numbers are 20 and 24.
Example Question #3 : Setting Up Equations
Set up an equation that properly displays the information given.
Suzanne has a pack of multi-colored jelly beans. She wants to sort them into equal amounts to give out to her four friends, but not until she eats eight of them. If the total pack contains 60 jelly beans, then how many is each friend going to get?
Let be the number of jelly beans that each friend will receive. She has four friends, so the total number of jelly beans her friends will receive is
. Suzanne eats another eight, so the equation can be written as
.
Example Question #1 : Equations
What is the equation of the line that has a slope of 3 and passes through the point (3,-6)?
The equation for a line in slope-intercept form is:
where and
are the known coordinates (3,-6).
Substituting gives
,
and simplifying gives the final answer:
Example Question #1 : Setting Up Equations
Your friend goes on a diet to lose a little weight. He starts at pounds and cuts his calories by
a day. Write a linear equation to express your friend's weight in pounds as a function of weeks on the diet. Hint: there are
,
calories in a pound.
The question asks for a relation between pounds lost and weeks on the diet. If each day your friend cuts 500 calories, the number of pounds he is losing per week is 1:
The rate of change, or slope, is therefore -1. The slope is negative because the independent variable (weight in pounds) is decreases as the dependent variable (time in weeks) increases. The y-intercept is 180, because that is how much your friend weighs at the start, when time = 0. Plugging these values into form, we end up with:
Example Question #6 : Setting Up Equations
A circular tower stands surrounded by a circular moat. A bridge provides a passage over the moat to the tower. The distance from the outer edge of the moat to the center of the tower is meters. The area of the floor of tower is
. How long is the bridge over the moat?
The distance from the outer edge of the moat to the center of the castle is the radius (100 m) of the larger circle formed by the outer edge of the circular moat.
The radius of the tower's floor (found using the area of the floor), needs to be subracted from 100 m to find the distance fo the bridge.
Example Question #1 : Equations
The monthly cost to insure your cars varies directly with the number of cars you own. Right now, you are paying $420 per month to insure 3 cars, but you plan to get 2 more cars, so that you will own 5 cars. How much does it cost to insure 5 cars monthly?
The statement, 'The monthly costly to insure your cars varies directly with the number of cars you own' can be mathematically expressed as . M is the monthly cost, C is the number of cars owned, and k is the constant of variation.
Given that it costs $420 a month to insure 3 cars, we can find the k-value.
Divide both sides by 3.
Now, we have the mathematical relationship.
Finding how much it costs to insure 5 cars can be found by substituting 5 for C and solving for M.
Example Question #8 : Setting Up Equations
Express as an equation.
more than
is
Take every word and translate into math.
more than means that you need to add
to something which is
.
Anytime you see "is" means equal.
Now let's combine and create an expression of
Example Question #9 : Setting Up Equations
Express as an equation.
times
is
less than
Take every word and translate into math.
times something means that you need to multiply
to something which is
.
less than means that you need to subtract
from
.
Anytime you see "is" means equal.
Let's combine to get .
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