All High School Math Resources
Example Questions
Example Question #1 :Setting Up Equations
汤姆is painting a fencefeet long. He starts at the West end of the fence and paints at a rate offeet per hour. Afterhours, Huck joins Tom and begins painting from the East end of the fence at a rate offeet per hour. Afterhours 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?
汤姆paints for a total ofhours (2 on his own, 2 with Huck's help). Since he paints at a rate offeet 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 fencefeet gives the length of the fence Tom will NOT paint:feet. If Huck finishes the job, he will paint thatfeet of the fence. Using, we can determine how long this will take Huck to do:
hours.
If Huck workshours and Tom workshours, he worksmore hours than Tom.
Example Question #2 :Equations
Simplify the fraction to the lowest terms:
Cannot be simplified
Find the common multiple between the numerator and denominator.
divide numerator and denominator by 3:
divide numerator and denominator by 7:
divide numerator and denominator by 4:
Cannot be divided any more- lowest terms.
Example Question #1 :Equations
Solve the following equation for x in terms of the other variables:
Multiply both sides byto get:
Distribute the:
Combine like terms:
Divide both sides by:
Example Question #1 :Equations
Solve the following equation for x in terms of the other variables:
Divide both sides by:
Example Question #1 :Basic Single Variable Algebra
If given the equation, witha positive integer, the result must be an integer multiple of:
5
12
2
8
10
5
The mathematical expression given in the question is. Adding together like terms,, this can be simplified to. The expressioncan be factored as. For every positive integer,must be a multiple of 5. If, then,这不是一个整数2的倍数,8日,10日,或15. Therefore, the correct answer is 5.
Example Question #1 :Solving Equations
Cindy's Cotton Candy sells cotton candy by the bag. Her monthly fixed costs are. It coststo make each bag and she sells them for.
What is the monthly break-even point?
The break-even point occurs when the.
The equation to solve becomes
so the break-even point is.
Example Question #7 :Equations
Cindy's Cotton Candy sells cotton candy by the bag. Her monthly fixed costs are. It coststo make each bag and she sells them for.
To make a profit of有多少袋必须卖棉花糖?
So the equation to solve becomes, ormust be sold to make a profit of.
Example Question #8 :Equations
Solve forandto satisfy both equations in the system:
,
,
,
,
,
,
The two equations in this system can be combined by addition or subtraction to solve forand. Isolate thevariable to solve for it by multiplying the top equation byso that when the equations are combined theterm disappears.
Divide both sides byto findas the value for.
Substitutingforin both of the two equations in the system and solving forgives a value offor.
Example Question #9 :Equations
Solve for:
Rewriteas a compound statement and solve each part separately:
The solution set is
Example Question #10 :Equations
and. What is the value of?
65
112
130
25
33
65
First, notice that we can factorinto the form (a-b)(a+b). We are told that a-b=3, so we can substitute that into the first equation.
If we divide both sides by 3, we can obtain the value of a+b.
We now have a system of equations: a-b = 3, a+b = 11. We will solve this system by elimination. If we add the two equations together, we obtain the following:
.
Divide both sides by 2.
Going back to the equation a-b = 7, we can solve for b.
Add b to both sides.
Subtract 3 from both sides.
Ultimately, the question asks us to determine the value of.
=.
The answer is 65.
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