ISEE Middle Level Math : Equations

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

Example Question #2673 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve the equation:

\displaystyle 4^{2}+5^{3}

Possible Answers:

\displaystyle 143

\displaystyle 141

\displaystyle 145

\displaystyle 140

Correct answer:

\displaystyle 141

Explanation:

To solve, first find the exponents:

\displaystyle 4^{2}=16

\displaystyle 5^{3}=125

Then solve the equation:\displaystyle 16+125=141

Answer: \displaystyle 141

Example Question #2674 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve the equation:

\displaystyle 6^{3}-4^{3}

Possible Answers:

\displaystyle 152

\displaystyle 64

\displaystyle 276

\displaystyle 216

Correct answer:

\displaystyle 152

Explanation:

To solve, first find the exponents:

\displaystyle 6^{3}=216

\displaystyle 4^{3}=64

Then solve the equation: \displaystyle 216-64=152

Answer: \displaystyle 152

Example Question #2675 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve for x in the following equation:

\displaystyle x-4=5

Possible Answers:

\displaystyle x=4

\displaystyle x=54

\displaystyle x=5

\displaystyle x=9

\displaystyle x=3

Correct answer:

\displaystyle x=9

Explanation:

To solve for x, we want to get x to stand alone or be by itself.  So in the equation

\displaystyle x-4=5

we want x to be alone.  To do that, we must cancel out the -4 with it.  To cancel -4, we must add 4.  If we add 4 to the left side of the equal sign, we must add 4 to the right side.  So,

\displaystyle x-4+4=5+4

\displaystyle x+0=9

\displaystyle x=9

Example Question #2675 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve for \displaystyle n:

\displaystyle 45n=225

Possible Answers:

\displaystyle 50

\displaystyle 6

\displaystyle 5

\displaystyle 45

\displaystyle 15

Correct answer:

\displaystyle 5

Explanation:

In order to solve this equation we need to isolate the variable to one side. Do not forget to perform the same operation on both sides of the equation.

\displaystyle 45n=225

Divide each side of the equation by \displaystyle 45:

\displaystyle \frac{45n}{45}=\frac{225}{45}

Solve.

\displaystyle n=5

 

Example Question #2676 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve for t:

\displaystyle 22t=352

Possible Answers:

\displaystyle 15

\displaystyle 16

\displaystyle 374

\displaystyle 330

Correct answer:

\displaystyle 16

Explanation:

To solve, divide both sides by 22:

\displaystyle 22t\div 22=352\div 22

\displaystyle t=16

Answer: \displaystyle 16

Example Question #2677 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve for b:

\displaystyle 35b=525

Possible Answers:

\displaystyle 15

\displaystyle 560

\displaystyle 490

\displaystyle 14

Correct answer:

\displaystyle 15

Explanation:

To solve, divide each side by 35:

\displaystyle 35b\div 35=525\div 35

\displaystyle b=15

Answer: \displaystyle 15

Example Question #2678 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve: \displaystyle 12^{2}\div 4^{2}=

Possible Answers:

\displaystyle 9

\displaystyle 16

\displaystyle 6

\displaystyle 3

Correct answer:

\displaystyle 9

Explanation:

To solve, find solve the exponents:

\displaystyle 12^{2}=144

\displaystyle 4^{2}=16

Then solve: \displaystyle 144\div 16=9

Answer: \displaystyle 9

Example Question #2679 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve:

\displaystyle 10^{3}\div 40=

Possible Answers:

\displaystyle 40

\displaystyle 25

\displaystyle 960

\displaystyle 1040

Correct answer:

\displaystyle 25

Explanation:

To solve, first solve the exponents:

\displaystyle 10^{3}=1000

Then solve,

\displaystyle 1000\div 40=25

Answer: \displaystyle 25

Example Question #1 : Word Problems

Mark is three times as old as his son Brian. In ten years, Mark will be \displaystyle 43 years old. In how many years will Mark be twice as old as Brian? 

Possible Answers:

\displaystyle 17

\displaystyle 22

\displaystyle 13

\displaystyle 11

\displaystyle 20

Correct answer:

\displaystyle 11

Explanation:

In ten years, Mark will be \displaystyle 43 years old, so Mark is \displaystyle 43-10 = 33 years old now, and Brian is one-third of this, or \displaystyle 33 \div 3 = 11 years old. 

Let \displaystyle N be the number of years in which Mark will be twice Brian's age. Then Brian will be \displaystyle N + 11, and Mark will be \displaystyle N + 33. Since Mark will be twice Brian's age, we can set up and solve the equation:

\displaystyle 2 (N + 11) = N + 33

\displaystyle 2N + 22 = N + 33

\displaystyle 2N + 22-N - 22 = N + 33 -N - 22

\displaystyle N = 11

Mark will be twice Brian's age in \displaystyle 11 years.

Example Question #1 : Word Problems

Gary is twice as old as his niece Candy. How old will Candy will be in five years when Gary is \displaystyle 37 years old?

Possible Answers:

Not enough information is given to determine the answer.

\displaystyle 21

\displaystyle 24

\displaystyle 14

\displaystyle 16

Correct answer:

\displaystyle 21

Explanation:

Since Gary will be 37 in five years, he is \displaystyle 37 - 5 = 32 years old now. He is twice as old as Cathy, so she is \displaystyle 32 \div 2 =16 years old, and in five years, she will be \displaystyle 16 + 5 = 21 years old.

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