ISEE Middle Level Math : Equations

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

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Example Questions

Example Question #1 : Equations

 

 

\(\displaystyle 3a+8+7=14\times 3=\)

Possible Answers:

\(\displaystyle 27\)

\(\displaystyle 18\)

\(\displaystyle 3\)

\(\displaystyle 9\)

\(\displaystyle 81\)

Correct answer:

\(\displaystyle 9\)

Explanation:

To solve: 

First, solve both equations on each end, keeping the variable.

\(\displaystyle \small 3a+ 8+ 7 = 14\cdot 3\)

\(\displaystyle 3a + 15= 42\)

Then, subtract 15 from each side of the equation.

\(\displaystyle 3a +15-15=42-15\)

\(\displaystyle 3a =27\)

Finally, divide each side by 3 so that only the variable remains.

\(\displaystyle \small 3a\div 3=27\div 3\)

\(\displaystyle \small \small a=9\)

Example Question #1 : How To Find The Solution To An Equation

Ann, Bailey, Cara, Jack, and Jill are running a marathon.  Cara finishes 4 minutes before Ann.  Jill finishes after Bailey, who finishes after Ann.  Jack finishes right before Bailey.  Who else does Jack finish the race before?

Possible Answers:

Cara

Bailey

Jill

Ann

There is not enough information to solve this problem.

Correct answer:

Jill

Explanation:

Cara finishes first.  Ann and Bailey finish before Jill.  If Jack finishes right before Bailey, then Jill finishes last.

Example Question #2 : How To Find The Solution To An Equation

Solve for \(\displaystyle n\):

\(\displaystyle 7n + 19 = 82\)

Possible Answers:

\(\displaystyle n = 10\)

\(\displaystyle n = 7\)

\(\displaystyle n=6\)

\(\displaystyle n = 9\)

\(\displaystyle n = 8\)

Correct answer:

\(\displaystyle n = 9\)

Explanation:

Subtract 19, then divide by 7:

\(\displaystyle 7n + 19 = 82\)

\(\displaystyle 7n + 19-19 = 82-19\)

\(\displaystyle 7n = 63\)

\(\displaystyle 7n \div 7= 63 \div 7\)

\(\displaystyle n = 9\)

Example Question #3 : How To Find The Solution To An Equation

 

 

 

A bicycle originally costs $120.00. If it is on sale for 30% off, what is the sale price of the bicycle?

Possible Answers:

\(\displaystyle \$84.00\)

\(\displaystyle \$90.00\)

\(\displaystyle \$156.00\)

\(\displaystyle \$117.00\)

Correct answer:

\(\displaystyle \$84.00\)

Explanation:

First multiply the original price by 30%.

\(\displaystyle 120\ast .30=36\)

Then subtract that amount from the original price.

\(\displaystyle 120-36=84\)

The sale price is $84.00

Example Question #3 : How To Find The Solution To An Equation

\(\displaystyle 8\cdot \left ( 2\cdot 5 \right ) \div \left ( 4\cdot 1 \right )=\)

Possible Answers:

\(\displaystyle 14\)

\(\displaystyle 32\)

\(\displaystyle 20\)

\(\displaystyle 24\)

Correct answer:

\(\displaystyle 20\)

Explanation:

First solve the parentheses.

\(\displaystyle 8 * 10 \div 4=\)

Then solve from left to right since multiplication and division are interchangeable:

\(\displaystyle 80\div 4=20\)

The answer is 20.

Example Question #1 : Equations

\(\displaystyle 3 \frac{2}{6} \ast 2\frac{3}{4}=\)

Possible Answers:

\(\displaystyle 9\)

\(\displaystyle 3\)

\(\displaystyle 9 \frac{1}{6}\)

\(\displaystyle 22\frac{1}{6}\)

Correct answer:

\(\displaystyle 9 \frac{1}{6}\)

Explanation:

First, convert each mixed number into an improper fraction.

\(\displaystyle \frac{20}{6}\ast \frac{11}{4}\)

Then, reduce where possible and multiply.

Finally, convert your answer into a mixed-number fraction.

\(\displaystyle \frac{55}{6}=9 {\frac{1}{6}}\)

Example Question #1 : How To Find The Solution To An Equation

\(\displaystyle 11 \frac{1}{4} \div 5\frac{2}{5}=\)

Possible Answers:

\(\displaystyle 3\)

\(\displaystyle 2\)

\(\displaystyle 2\frac{1}{18}\)

\(\displaystyle 8\)

\(\displaystyle 2 \frac{1}{12}\)

Correct answer:

\(\displaystyle 2 \frac{1}{12}\)

Explanation:

First, convert each mixed number into an improper fraction and flip the second fraction. Then, change the operation to multiplication:

\(\displaystyle \frac{45}{4} \ast \frac{5}{27}=\)

Reduce where possible and multiply. Convert your answer into a mixed fraction.

Example Question #1 : Equations

\(\displaystyle 8^{3}\div 2^{2}=\)

Possible Answers:

\(\displaystyle 23\)

\(\displaystyle 12\)

\(\displaystyle 128\)

\(\displaystyle 34\)

Correct answer:

\(\displaystyle 128\)

Explanation:

First find the exponent value for each number:

\(\displaystyle 8^{3}\div 2^{2}=512 \div 4=\)

Then divide accordingly. The answer is 128.

Example Question #5 : How To Find The Solution To An Equation

\(\displaystyle 11+39=12+28+2a\)

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 20\)

\(\displaystyle 10\)

\(\displaystyle 2.5\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 5\)

Explanation:

First follow order of operations and solve on each side.

\(\displaystyle 11+39=12+28+2a\)

\(\displaystyle 50=40+2a\)

Then, subtract 40 from each side to leave only the variable:

\(\displaystyle 50-40=40+2a-40\)

\(\displaystyle 10=2a\)

Finally, divide both sides by 2.

\(\displaystyle 10\div 2=2a\div 2\)

The answer is \(\displaystyle 5=a\)

Example Question #2 : Equations

\(\displaystyle 13 + 27=12+3+ 5a\)

Possible Answers:

\(\displaystyle 3\)

\(\displaystyle 5.5\)

\(\displaystyle 6\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 5\)

Explanation:

First solve with order of operations on each side:

\(\displaystyle 13 + 27=12+3+ 5a\)

\(\displaystyle 40 = 15+5a\)

Then subtract 15 from each side:

\(\displaystyle 40-15=15+ 5a-15\)

\(\displaystyle 25=5a\)

Finally, divide each side by 5:

\(\displaystyle 25\div 5=5a\div 5\)

\(\displaystyle 5=a\)

The answer is 5.

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