Setting Up Equations - Algebra II

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.

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 .

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.

In math, i is equal to the square root of -1. You can do most regular mathematical operations with it.

To simplify the expressions, you would do the following:

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.

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:

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 .

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.

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:

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, .

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

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 .

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 .

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:

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 .

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:

You know that shirts sell for 15 dollars and jeans sell for 30 dollars.

The tricky part is knowing that you sold at least 200 dollars worth of merchandise.

This means that you could have sold more than 200 dollars, but no less than that.

This means that your answer 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 .

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 .

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 .