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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1861 : Sat Mathematics

Translate into an algebraic expression:

One third of the difference of a number and 3 equals five times the number.

Possible Answers:

$\frac{1}{3}\left ( x+3 \right )= 5x$

$\frac{1}{3}x-3=5$

$\frac{1}{3}\left ( x-3 \right )=5x$

$\frac{1}{3}x-3=5x$

$3\left ( x-3 \right )=5x$

Correct answer:

$\frac{1}{3}\left ( x-3 \right )=5x$

Explanation:

You have to form the difference first and must be enclosed in parentheses which gets multiplied by 1/3. The word "equals" means the "=" symbol

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Example Question #84 : Algebra

Translate into an algebraic expression:

Two fifths of the difference of five times a number and two equals six times the number.

Possible Answers:

$\frac{2}{5}(2x+5)=6x$

$\frac{2}{5}(5x-2)=6x$

$\frac{2}{5}(2x-5)=6x$

$\frac{2}{5}(2-5x)=6x$

$\frac{2}{5}(5x+2)=6x$

Correct answer:

$\frac{2}{5}(5x-2)=6x$

Explanation:

In order to translate the description into an algebraic expression, you must first form the difference (5x-2) , multiply it by $\frac{2}{5}$ , and then set the equation equal to , as follows:

$\frac{2}{5}(5x-2)=6x$

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Example Question #85 : Algebra

Translate into an algebraic expression:

Three halves of the difference between six and eight times a number is equal to four times a number.

Possible Answers:

$\frac{3}{2}(6+8x)=4x$

$\frac{3}{2}(6-8x)=4x$

$\frac{3}{2}(6\times 8x)=4x$

$\frac{3}{2}(8x-6)=4x$

$\frac{3}{2}(6-8)x=4x$

Correct answer:

$\frac{3}{2}(6-8x)=4x$

Explanation:

In order to translate the sentence into an algebraic expression, first create the difference (6-8x) , multiply it by $\frac{3}{2}$ , and set the expression equal to , as follows:

$\frac{3}{2}(6-8x)=4x$

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Example Question #85 : Algebra

78 - | 6x - 13| = 100

Give the solution set.

Possible Answers:

The equation has no solution.

$x = 1\frac{1}{2}$ or $x =- 3 \frac{8}{9}$

$x = -1\frac{1}{2}$ or $x =- 3 \frac{8}{9}$

$x = -1\frac{1}{2}$ or $x = 3 \frac{8}{9}$

$x = 1\frac{1}{2}$ or $x = 3 \frac{8}{9}$

Correct answer:

The equation has no solution.

Explanation:

78 - | 6x - 13| = 100

78 - | 6x - 13| - 78 = 100 - 78

-| 6x - 13| = 22

| 6x - 13| = -22

However, the absolute value of an expression cannot be a negative number. Therefore, this statement is false regardless of the value of , and the original equation has no solution.

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Example Question #86 : How To Find The Solution To An Equation

18+ | 16 - 4x| = 100 .

Give the solution set.

Possible Answers:

$x = 16\frac{1}{2}$ or $x = 24\frac{1}{2}$

$x = -16\frac{1}{2}$ or $x = 24\frac{1}{2}$

The equation has no solution.

$x = -16\frac{1}{2}$ or $x =- 24\frac{1}{2}$

$x = 16\frac{1}{2}$ or $x =- 24\frac{1}{2}$

Correct answer:

$x = -16\frac{1}{2}$ or $x = 24\frac{1}{2}$

Explanation:

18+ | 16 - 4x| = 100

18+ | 16 - 4x| - 18 = 100 - 18

| 16 - 4x| = 82

Either 16-4x= -82 or 16-4x= 82 . Solve them separately:

16-4x= -82

16-4x - 16 = -82 - 16

-4x= -98

$\frac{-4x}{-4}= \frac{-98}{-4}$

$x = 24\frac{1}{2}$

16-4x= 82

16-4x - 16 = 82 - 16

-4x = 66

$\frac{-4x}{-4}= \frac{66}{-4}$

$x = -16\frac{1}{2}$

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Example Question #86 : Algebra

-8 |7 f - 12 | = 232 .

Give the solution set.

Possible Answers:

$f = 2\frac{3}{7}$ or $f = -5 \frac{6}{7}$

$f =- 2\frac{3}{7}$ or $f = -5 \frac{6}{7}$

The equation has no solution.

$f = 2\frac{3}{7}$ or $f = 5 \frac{6}{7}$

$f =- 2\frac{3}{7}$ or $f = 5 \frac{6}{7}$

Correct answer:

The equation has no solution.

Explanation:

-8 |7 f - 12 | = 232

$\frac{-8 |7 f - 12 | }{-8}= \frac{232}{-8}$

|7 f - 12 | = -29

However, the absolute value of an expression cannot be a negative number. Therefore, this statement is false regardless of the value of , and the original equation has no solution.

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Example Question #91 : Algebra

| 3y - 17| + 12 = 49 .

Which of the following is a solution of this equation?

Possible Answers:

$y = -14\frac{2}{3}$

$y = 14\frac{2}{3}$

y = -18

y = 26

$y = -6 \frac{2}{3}$

Correct answer:

$y = -6 \frac{2}{3}$

Explanation:

To solve for the variable we must move all constants to the other side of the equation. Since we have absolute value bars in the particular equation we will first move all constants that are outside of the absolute value bars. To do this apply the oppisite operation. In this particular case, subtract twelve from both sides.

| 3y - 17| + 12 = 49

| 3y - 17| + 12 - 12 = 49 - 12

| 3y - 17| = 37

Now we will deal with the absolute value bars which state that the quantity inside them can be positive of negative.

Either

3y - 17= -37 or 3y - 17= 37 .

Solve each separately:

3y - 17= -37

3y - 17+ 17 = -37 + 17

3y = -20

$\frac{3y}{3} = \frac{-20}{3}$

$y = -6 \frac{2}{3}$

3y - 17= 37

3y - 17+17 = 37+17

3y = 54

$\frac{3y}{3} = \frac{54}{3}$

y = 18

Therefore, $y = -6 \frac{2}{3}$ or y = 18 .

The correct choice is $y = -6 \frac{2}{3}$ .

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Example Question #92 : Algebra

125 - |4t-98| = 113

Give the solution set to this equation.

Possible Answers:

$t= -21\frac{1}{2}$ or $t= -27\frac{1}{2}$

$t= -21\frac{1}{2}$ or $t= 27\frac{1}{2}$

$t= 21\frac{1}{2}$ or $t= 27\frac{1}{2}$

$t= 21\frac{1}{2}$ or $t= -27\frac{1}{2}$

The equation has no solution.

Correct answer:

$t= 21\frac{1}{2}$ or $t= 27\frac{1}{2}$

Explanation:

125 - |4t-98| = 113

125 - |4t-98| - 125 = 113 - 125

- |4t-98| =-12

|4t-98| =12

4t-98 = -12 or 4t-98 = 12

Solve separately:

4t-98 = -12

4t-98 + 98 = -12 + 98

4t = 86

$\frac{4t}{4} = \frac{86 }{4}$

$t= 21\frac{1}{2}$

4t-98 = 12

4t-98 + 98 = 12 + 98

4t = 110

$\frac{4t}{4} = \frac{110 }{4}$

$t= 27\frac{1}{2}$

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Example Question #91 : How To Find The Solution To An Equation

James is an artist and makes number of portraits per month. At this rate, how many months will it take him to paint portraits?

Possible Answers:

$\frac{t}{p}$

10t

$\frac{100p}{t}$

$\frac{p}{t}$

Correct answer:

$\frac{t}{p}$

Explanation:

To figure out the total portraits done by James, you must multiply rate by the number of months . This equation would be pm=t . To solve for the number of months you must divide both sides by . This gives us $m=\frac{t}{p}$ .

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Example Question #94 : Algebra

Point lies on the line with the equation y-2=8(x-3) . If the -coordinate for is , what is the -coordinate?

Possible Answers:

Correct answer:

Explanation:

The first step is to simplify your equation. You distribute to get y-2=8x-24 . Then to get by itself you add to both sides ending with y=8x-22 . Finally insert the -coordinate to get 8(5)-22 which equals .

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1861 : Sat Mathematics

Example Question #84 : Algebra

Example Question #85 : Algebra

Example Question #85 : Algebra

Example Question #86 : How To Find The Solution To An Equation

Example Question #86 : Algebra

Example Question #91 : Algebra

Example Question #92 : Algebra

Example Question #91 : How To Find The Solution To An Equation

Example Question #94 : Algebra

All SAT Math Resources

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