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SAT Math : How to find the solution to an equation

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Example Questions

Example Question #101 : Algebra

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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. $\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where (x_1,y_1), (x_2, y_2) are points on the line.

So we will pick (-5, 80) , and (5, -60) .

$\text{Slope}=\frac{-60-80}{5-(-5)}=\frac{-140}{10}=-14$

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Example Question #102 : Algebra

$\begin{tabular}{cccccc} Time 0 & Time 1 & Time 2 & Time 3 & Time 4 & Time 5\\ \hline 1000& 500 & 250 & 125 & 62.5 & 31.25 \end{tabular}$

What equation best represents the following table?

Possible Answers:

$y=1000\left(\frac{1}{2}\right )^{-t}$

$y=\left(\frac{1}{2}\right )^t$

$y=1000\left(\frac{1}{2}\right )^t$

$y=1000\left(2\right)^t$

$y=1000\left(-\frac{1}{2}\right )^t$

Correct answer:

$y=1000\left(\frac{1}{2}\right )^t$

Explanation:

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

$\frac{\text{Time 1}}{\text{Time 0}}=\frac{500}{1000}=\frac{1}{2}$

$\frac{\text{Time 2}}{\text{Time 1}}=\frac{250}{500}=\frac{1}{2}$

$\frac{\text{Time 3}}{\text{Time 2}}=\frac{125}{250}=\frac{1}{2}$

$\frac{\text{Time 4}}{\text{Time 3}}=\frac{62.5}{125}=\frac{1}{2}$

$\frac{\text{Time 5}}{\text{Time 4}}=\frac{31.25}{62.5}=\frac{1}{2}$

We can that the common ratio is $\frac{1}{2}$ .

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,

y=c(1-r)^t , where is the starting amount, is the common ratio and is time.

After plugging our numbers in, we get

$y=1000\left( 1-\frac{1}{2}\right )^t$

$y=1000\left(\frac{1}{2}\right )^t$

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

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: C(x) = 10x +350

Revenues: R(x) = 35x

Thus, 10x + 350 = 35x

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

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Example Question #104 : 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

$8 = 3 + \sqrt{a}$

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

As you can see,

$5 = \sqrt{a}$ and

25 = a

So, the value of the unknown number is 25.

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

Solve

$\frac{4x-4}{x+4}=10$

Possible Answers:

$x=-\frac{22}{3}$

x=-3

x=-22

$x=\frac{22}{3}$

Correct answer:

$x=-\frac{22}{3}$

Explanation:

$\frac{4x-4}{x+4}=10$

First multiply by the denominator on each side

$\frac{4x-4}{x+4}\cdot(x+4)=10(x+4)$

4x-4=10(x+4)

Expand left side, and solve for

4x-4=10x+40

-44=6x

$x=\frac{-44}{6}=-\frac{22}{3}$

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SAT Math : How to find the solution to an equation

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #101 : Algebra

Example Question #102 : Algebra

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

Example Question #104 : Algebra

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

All SAT Math Resources

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