All Algebra II Resources
Example Questions
Example Question #11 : Setting Up Equations
If Bob's age is years old and Jack is
more than
times Bob's age, then express Jack's age in terms of
.
Take every word and translate into math.
more than means that you need to add
to something.
times something means that you need to multiply
to Bob's age which is
.
Now we can combine them to have an expression of .
Example Question #11 : Setting Up Equations
There are marbles in a jar. There are
types of color: red, blue, green and yellow. There are
red marbles,
blue marbles,
green marbles. Find an equation to represent the number of yellow marbles.
We have known values and
unknown value. We have a total and that these
colors add up to
.
Let's represent the colors with variables corresponding to the first letter of the color. .
Now, plug in the values that are known. Final answer is .
To simplify we add the constants which results in:
Example Question #11 : Setting Up Equations
Express as an equation.
Difference between times
and the quotient of
and
is
more than
times
.
Take every word and translate into math. What a difference means, is that is the first number subtracting
.
The part is
times something means that you need to multiply
to something which is
.
The part is quotient.
Anytime you take a quotient of and
,
is the in the numerator and
is in the denominator. Therefore the expression is
.
Anytime you see "is" means equal.
more than means that you need to add
to something.
That something is multipled by
or
.
Let's just combine them to have an expression of .
Example Question #14 : Setting Up Equations
Jon needs to make four monthly deposits. The first month, he deposits dollars. Each month after he adds
dollars to the previous month's deposit. Find an equation to solve for
if the total amount of money deposited for the four months is
Let's translate into math equations.
First month is Then for the next month, he adds
to the previous month or
Then, for the next month, he adds another
to the previous month which was
By adding another
, this month becomes
For the fourth month, it's just another
added to the previous month which was
The fourth month becomes
.
With the total given, lets combine the expressions to get .
Simplifying this we get:
Example Question #11 : Setting Up Equations
Express as an equation.
The sum of and
is
.
Take every word and translate into math. The sum of something means adding. So that would be . Is means equals something. Putting it all together, we get
.
Example Question #11 : Equations
Express as an equation.
The difference between and
is
Take every word and translate into math. Difference means subtracting. So we are subtracting and
. Is means equal something. Putting it all together, we have
.
Example Question #17 : Setting Up Equations
Express as an equation. The product of and
is the sum of
and
.
Take every word and translate into math. The product of something means multiplying. So we have . The sum of something means adding. So that would be
. Is means equals something. Putting it together, we have
.
Example Question #11 : Equations
Express as an equation. The quotient of and
is the difference of
and
times sum of
and
.
Take every word and translate into math. Quotient means dividing, so we have . When it's
and
,
will always be at the numerator of the fraction. Is means equal something. Difference is subtracting and we are subtracting
with
times sum of
and
. Times means multiplying and sum means addition. We are multiplying
with
. There must be parentheses as the sum of
and
is an expression. Putting it all together, we get
.
Example Question #19 : Setting Up Equations
Express as an equation.
The square root of is the sum of
and
squared.
Take every word and translate into math. Square root means using a radical sign. So we have . Is means equal something. Next, sum is addition so we have
. Since it's squared, we have the whole thing in parentheses raised to the second power like so:
. It is tempting to think it's
but if it was, then it should say sum of
and
square. So final answer is
.
Example Question #11 : Equations
Solve for in the following equation:
Starting with the equation , you want to collect like terms.
Put all of the numbers on one side, and leave only the variable on the other side.
The first step is to subtract from both sides.
You get .
The next step is to divide both sides by to get the final answer,
.
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