When 240 liters of oil were added to the barrel, the barrel's volume increased by . Therefore, of the barrel's capacity must equal 240 liters. If is the barrel's capacity, then . Solving for this equation gives you a solution of 640, which is the barrel's capacity.

First, we have to translate the question into an equation. So we have two integers. Let's call one of the integers .  The second integer is 5 times greater than the other one. Thus, we call this .  Both  and  are suppose to add up to 66. So mathematically, this is written as

We just solve for .

So the value of the integer is 11.

We will call this other integer .  Since the first integer is 2 units less than this other one, it is written as .  Both  and  add up to 84.  This is mathematically written as

Solve for .

The expression representing nickels and dimes making up $19.80 is

Where  is the number of nickels and  is the number of dimes. Notice that the number of nickels and dimes are multiplied by their values (i.e.  is multiplied by 0.05 because each nickel is worth 5 cents).  It is given that there are 15 more nickels than there are dimes.  This is represented as

and thus,

We can find the number of dimes by solving for .

So there are 127 dimes in the jar. Use this to find the number of nickels

So there are 142 nickels and 127 dimes in the jar.

The function is not defined when  and . 

It is defined between

and

1) First step in writing an equation is always to define variables:

total earnings left after subtracting gas money

miles driven

2) Look at the given information. We know Janet starts with $800. So that must be included in an equation detailing how to get from her initial income to her final earnings, and it cannot be dependent on anything, since she already has it:

3) We know she has to subtract gas money, and that the rate is $0.50 per mile, so:

4) It says that Janet must save ten percent. But the equation is only required to express the amount of money she earns prior to saving, so the ten percent is irrelevant to the equation.

So the final answer is

Let  represent the number.  

"Eight minus three times a number" can be written as: .  

"is" means equals or "".  

"4 less than 6 times that number" can be understood to mean 6 times a number minus 4, or .  

Putting these statements together gives:

When we combine like terms, we have to always first follow the order of operations (PEMDAS = parentheses, exponents, multiplication, division, addition, subtraction). So, we must first simplify what is inside the parentheses, then the exponents, the multiplication and division, then addition and subtraction. Don't forget to simplify like terms!

Here is the expression given: .

To simplify, follow the order of operations. 

Distribute through the terms in the inner parentheses:

Now distribute  into the terms of the remaining parentheses. Remember that  multiplied by itself produces , but  multiplied by  produces :

Complete the multiplication to finish expanding:

Add like terms to reach the answer:

The instructions tell us that the x-axis represents the number of loaves of bread sold and the y-axis represents net profit. 

Based upon this information, the $15 loss in profit when 0 loaves of bread are sold is the y-intercept of the equation, beacuse it represents the value of f(x=0).

So far, we know the y-intercept of our equation:

y = _x - 15

The word problem mentions that each loaf of bread sold generates $3 income. This represents the rise in the y-value in respect to the increase in the x-value, meaning this value is the slope of our equation:

y = 3x - 15