SAT Math : How to find the solution to an equation

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #11 : Linear / Rational / Variable Equations

If y = 4 and 6y = 10z + y, then z = ?

Possible Answers:

6

30

24

4

2

Correct answer:

2

Explanation:
  1. Substitute y in the equation for 4.
  2. You now have 6 * 4 = 10z + 4
  3. Simplify the equation: 24 = 10z + 4
  4. Subtract 4 from both sides: 24 – 4 = 10z + 4 – 4
  5. You now have 20 = 10z
  6. Divde both sides by 10 to solve for z.
  7. z = 2.

Example Question #71 : Linear / Rational / Variable Equations

A sequence of numbers is: 2, 5, 8, 11. Assuming it follows the same pattern, what would be the value of the 20th number?

Possible Answers:

56

55

61

59

50

Correct answer:

59

Explanation:

This goes up at a constant number between values, making it an arthmetic sequence. The first number is 2, with a difference of 3. Plugging this into the arithmetic equation you get A= 2 + 3 (n – 1). Plugging in 20 for n, you get a value of 59.

Example Question #112 : Algebra

The first four numbers of a sequence are 5, 10, 20, 40. Assuming the pattern continues, what is the 6th term of the sequence?

Possible Answers:

140

50

80

160

60

Correct answer:

160

Explanation:

Looking at the sequence you can see that it doubles each term, making it a geometric sequence. Since it doubles r = 2 and the first term is 5. Plugging this into the geometric equation you get A= 5(2)n–1. Setting n = 6, you get 160 as the 6th term.

Example Question #1791 : Sat Mathematics

Given f(x) = x– 9. What are the zeroes of the function?

Possible Answers:

–3, 0, 3

0

3

0, 3

–3, 3

Correct answer:

–3, 3

Explanation:

The zeroes of the equation are where f(x) = 0 (aka x-intercepts). Setting the equation equal to zero you get x2 = 9. Since a square makes a negative number positive, x can be equal to 3 or –3.

Example Question #111 : Algebra

Give the lines y = 0.5x+3 and y=3x-2. What is the y value of the point of intersection?

Possible Answers:

2

6

3

7

4

Correct answer:

4

Explanation:

In order to solve for the x value you set both equations equal to each other (0.5x+3=3x-2). This gives you the x value for the point of intersection at x=2. Plugging x=2 into either equation gives you y=4.

Example Question #11 : Linear / Rational / Variable Equations

10 gallons of paint will cover 75 ft2. How many gallons of paint will be required to paint the area of a rectangular wall that has a height of 8 ft and a length of 24 ft? 

Possible Answers:

14.2 gallons 

22.8 gallons 

25.6 gallons 

17 gallons 

31.4 gallons 

Correct answer:

25.6 gallons 

Explanation:

First we need the area or the rectangle. 24 * 8 = 192. So now we know that 10 gallons will cover 75 ft2 and x gallons will cover 192 ft2. We set up a simple ratio and cross multiply to find that 75x = 1920.

x = 25.6

Example Question #13 : How To Find The Solution To An Equation

What number decreased by 7 is equal to 10 increased by 7?

Possible Answers:

15

10

17

24

27

Correct answer:

24

Explanation:

The best way to solve this problem is to translate it into an equation, "decreased" meaning subtract and "increased" meaning add:

x – 7 = 10 + 7

x = 24

Example Question #191 : Algebra

If a%b = (2b + 3a)/(6ab), what would have a greater value, 2%3 or 3%2?

Possible Answers:

They are the same

3%2

Cannot be determined

2%3

Correct answer:

3%2

Explanation:

First find 2%3 = (2 * 3 + 3 * 2)/(6 * 2 * 3) = 12/36 = 1/3, then 3%2 = (2 * 2 + 3 * 3)/(6 * 3 * 2) = 13/36 which is greater.

Example Question #73 : Equations / Inequalities

Function

Possible Answers:

0

–1

1

–1/2

1/2

Correct answer:

–1/2

Explanation:

 

Func_sol_2

 

Example Question #12 : Algebra

If 5 + x is 5 more than 5,what is the value of 2x?

Possible Answers:

20

5

10

15

Correct answer:

10

Explanation:

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2x = 10

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