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SAT Math : Linear / Rational / Variable Equations

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Example Question #101 : Algebra

Screen shot 2016 02 11 at 12.33.27 pm

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:

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

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

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

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

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

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 : 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: 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 #103 : 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 #101 : Algebra

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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Example Question #101 : Algebra

Rational_5

Possible Answers:

–1

–2

Correct answer:

Explanation:

Rational_2

Rational_3

Rational_4

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Example Question #51 : Gre Quantitative Reasoning

Linesmb1

Possible Answers:

–b/(m²– 1)

–bm/(m²+ 1)

–b/(m + 1)

b/(m²+ 1)

bm/(m²+ 1)

Correct answer:

b/(m²+ 1)

Explanation:

Linesmb5

Linesmb4

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Example Question #3 : How To Find The Solution To A Rational Equation With Lcd

In the equation below, , , and are non-zero numbers. What is the value of in terms of and ?

$\frac{1}{m^3}-\frac{1}{k^2}=\frac{1}{p}$

Possible Answers:

$m=(\frac{p+k^2}{2})^3$

$m=(\frac{p+k^2}{pk^2})^{\frac{1}{3}}$

$m=\frac{p^2k^3}{p+k^2}$

$m=(\frac{pk^2}{p+k^2})^{\frac{1}{3}}$

$m=p^{\frac{1}{2}}-k^{\frac{1}{3}}$

Correct answer:

$m=(\frac{pk^2}{p+k^2})^{\frac{1}{3}}$

Explanation:

Pkm_7-21-13

Pkm2_7-21-13

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Example Question #101 : Algebra

Solve for x:

$\frac{x+3}{7}=3$

Possible Answers:

x=0

x=18

x=24

x=42

x=6

Correct answer:

x=18

Explanation:

The first step is to cancel out the denominator by multiplying both sides by 7:

$7\cdot \frac{x+3}{7}=3\cdot7$

x+3=21

Subtract 3 from both sides to get by itself:

x+3-3=21-3

x=18

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Example Question #106 : Algebra

Solve for and using elimination:

2x+3y=5

-x-2y=-8

Possible Answers:

x=8 and y=4

$x=\frac{5}{2}$ and $y=\frac{5}{3}$

x=-8 and y=-4

x=14 and y=-11

x=-14 and y=11

Correct answer:

x=-14 and y=11

Explanation:

When using elimination, you need two factors to cancel out when the two equations are added together. We can get the in the first equation to cancel out with the in the second equation by multiplying everything in the second equation by :

2x+3y=5

2(-x-2y)=2(-8)

Now our two equations look like this:

2x+3y=5

-2x-4y=-16

The can cancel with the -2x , giving us:

3y=5

-4y=-16

These equations, when summed, give us:

-y=-11

y=11

Once we know the value for , we can just plug it into one of our original equations to solve for the value of :

2x+3y=5

2x+3(11)=5

2x+33=5

2x=-28

x=-14

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SAT Math : Linear / Rational / Variable Equations

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 : Algebra

Example Question #103 : Algebra

Example Question #101 : Algebra

Example Question #101 : Algebra

Example Question #51 : Gre Quantitative Reasoning

Example Question #3 : How To Find The Solution To A Rational Equation With Lcd

Example Question #101 : Algebra

Example Question #106 : Algebra

All SAT Math Resources

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