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Example Questions
Example Question #121 : How To Find The Solution To An Equation
A car averages miles per gallon. If gas costs
per gallon, which of the following is closest to how much the gas would cost for this car to travel
typical miles?
To solve this problem you should divide the total number of miles by the miles per gallon
, and then multiply by the cost of gas per gallon
. This gives you
, which is closest to
.
Example Question #121 : Equations / Inequalities
When , by how much does the value of
exceed the value of
?
You must plug in for
and
for
, this means
and
Example Question #121 : How To Find The Solution To An Equation
What is the value of when
?
The first step is to subtract from both sides so you're left with
. Next, you add
to both sides, giving you
. The final step is to divide by
, giving you
.
Example Question #1891 : Act Math
Karen has more than
times as many dollars as Susan. Karen also has
as many dollars as John would if he had
more dollars. How many dollars does Susan have, relative to John?
First, set up our two equations. If Karen has seven dollars more than three times as many dollars as Susan, then . If Karen has half as many dollars as John would if he had two more dollars, then
. The Substitution Property of Equality thus says that
. Now, we simply solve for
in terms of
.
Example Question #1892 : Act Math
If the third day of the year is a Wednesday, what is the 165th day?
Wednesday
Monday
Thursday
Tuesday
Friday
Thursday
If the third day is a Wednesday, then the first day is a Monday. 23 weeks will complete a cycle with the 161st day. Therefore, the fourth day past that, 165, is a Thursday.
Example Question #1 : How To Find The Solution To A Rational Equation With Lcd
John, Jill, and Jack are splitting a pizza. John eats of the pizza and Jill eats
of the pizza. How much of the pizza is left for Jack?
We can write an equation for the amount of pizza eaten, with as the amount left for Jack.
To solve this equation, we must find the lowest common denominator of and
. We can list the multiples of
and
to find the least common multiple:
We can see that the least common multiple of and
is
, so we can rewrite each of the fractions with a denominator of
.
When we put these fractions back into the equation, we can solve for :
Example Question #2 : How To Find The Solution To A Rational Equation With Lcd
What is the slope of a line represented by the equation:
To solve problems where you need to find the slope of a line in a given equation, change the equation so that it matches y-intercept form:
For this equation, first move the 3x over to the other side of the equation.
The equation should now look like this:
Then, divide by 15 to isolate the variable .
Then simplify
Whatever number is before the x in the equation (m) is your slope.
Example Question #103 : Algebra
–1
1
0
–2
2
2
Example Question #1 : How To Find The Solution To A Rational Equation With Lcd
b/(m2 + 1)
–b/(m2 – 1)
–b/(m + 1)
–bm/(m2 + 1)
bm/(m2 + 1)
b/(m2 + 1)
Example Question #2 : How To Find The Solution To A Rational Equation With Lcd
In the equation below, ,
, and
are non-zero numbers. What is the value of
in terms of
and
?
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