SAT Math : How to find the solution to an equation

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #101 : Linear / Rational / Variable Equations

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Calculate the slope of the line.

Possible Answers:

Correct answer:

Explanation:

In order to solve for the slope, we need to recall how to find the slope of a line. , where  are points on the line.

So we will pick , and .

Example Question #101 : How To Find The Solution To An Equation

 

What equation best represents the following table?

Possible Answers:

Correct answer:

Explanation:

The first step is to find the common ratio amongst the data. 

 

We can that the common ratio is .

Now we need to set up an equation that will give an answer for any time.

We can set up an exponential decay model, the general equation is,

, where  is the starting amount,  is the common ratio and  is time.

After plugging our numbers in, we get

 

Example Question #141 : Algebra

Sally sells custom picture frames.  Her monthly fixed costs are $350.  It costs $10 to make each frame.  Sally sells her picture frames for $35 each.

How many picture frames must Sally sell in order to break even?

Possible Answers:

Correct answer:

Explanation:

The break-even point is where the costs equal the revenues.

Let  = # of frames sold

Costs: 

Revenues: 

Thus,

So 14 picture frames must be sold each month to break-even.

Example Question #102 : Algebra

8 is 3 greater than the square root of an unknown number. What is the unknown number?

Possible Answers:

Correct answer:

Explanation:

In order to solve for the unknown number, you must write an equation and solve for a variable. 8 is 3 greater than the square root of an unknown number translates to

To solve for a you must subtract 3 from both sides, and then square both sides.

 

As you can see,

 and

So, the value of the unknown number is 25. 

Example Question #102 : How To Find The Solution To An Equation

Solve

Possible Answers:

Correct answer:

Explanation:

First multiply by the denominator on each side

Expand left side, and solve for 

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