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ISEE Middle Level Math : Equations

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

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All ISEE Middle Level Math Resources

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Example Questions

Example Question #1 : Equations

$3a+8+7=14\times 3=$ $\displaystyle 3a+8+7=14\times 3=$

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.

$\small 3a+ 8+ 7 = 14\cdot 3$ $\displaystyle \small 3a+ 8+ 7 = 14\cdot 3$

$\displaystyle 3a + 15= 42$

Then, subtract 15 from each side of the equation.

$\displaystyle 3a +15-15=42-15$

3a =27 $\displaystyle 3a =27$

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

$\small 3a\div 3=27\div 3$ $\displaystyle \small 3a\div 3=27\div 3$

$\small \small a=9$ $\displaystyle \small \small a=9$

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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.

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

Solve for $\displaystyle n$:

$\displaystyle 7n + 19 = 82$

Possible Answers:

n = 10 $\displaystyle n = 10$

n = 7 $\displaystyle n = 7$

n=6 $\displaystyle n=6$

n = 9 $\displaystyle n = 9$

n = 8 $\displaystyle n = 8$

Correct answer:

n = 9 $\displaystyle n = 9$

Explanation:

Subtract 19, then divide by 7:

$\displaystyle 7n + 19 = 82$

$\displaystyle 7n + 19-19 = 82-19$

7n = 63 $\displaystyle 7n = 63$

$7n \div 7= 63 \div 7$ $\displaystyle 7n \div 7= 63 \div 7$

n = 9 $\displaystyle n = 9$

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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:

$\$84.00$ $\displaystyle \$84.00$

$\$90.00$ $\displaystyle \$90.00$

$\$156.00$ $\displaystyle \$156.00$

$\$117.00$ $\displaystyle \$117.00$

Correct answer:

$\$84.00$ $\displaystyle \$84.00$

Explanation:

First multiply the original price by 30%.

$120\ast .30=36$ $\displaystyle 120\ast .30=36$

Then subtract that amount from the original price.

$\displaystyle 120-36=84$

The sale price is $84.00

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

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

Possible Answers:

$\displaystyle 14$

$\displaystyle 32$

$\displaystyle 20$

$\displaystyle 24$

Correct answer:

$\displaystyle 20$

Explanation:

First solve the parentheses.

$8 * 10 \div 4=$ $\displaystyle 8 * 10 \div 4=$

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

$80\div 4=20$ $\displaystyle 80\div 4=20$

The answer is 20.

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Example Question #1 : Equations

$3 \frac{2}{6} \ast 2\frac{3}{4}=$ $\displaystyle 3 \frac{2}{6} \ast 2\frac{3}{4}=$

Possible Answers:

$\displaystyle 9$

$\displaystyle 3$

$9 \frac{1}{6}$ $\displaystyle 9 \frac{1}{6}$

$22\frac{1}{6}$ $\displaystyle 22\frac{1}{6}$

Correct answer:

$9 \frac{1}{6}$ $\displaystyle 9 \frac{1}{6}$

Explanation:

First, convert each mixed number into an improper fraction.

$\frac{20}{6}\ast \frac{11}{4}$ $\displaystyle \frac{20}{6}\ast \frac{11}{4}$

Then, reduce where possible and multiply.

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

$\frac{55}{6}=9 {\frac{1}{6}}$ $\displaystyle \frac{55}{6}=9 {\frac{1}{6}}$

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

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

Possible Answers:

$\displaystyle 3$

$\displaystyle 2$

$2\frac{1}{18}$ $\displaystyle 2\frac{1}{18}$

$\displaystyle 8$

$2 \frac{1}{12}$ $\displaystyle 2 \frac{1}{12}$

Correct answer:

$2 \frac{1}{12}$ $\displaystyle 2 \frac{1}{12}$

Explanation:

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

$\frac{45}{4} \ast \frac{5}{27}=$ $\displaystyle \frac{45}{4} \ast \frac{5}{27}=$

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

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Example Question #1 : Equations

$8^{3}\div 2^{2}=$ $\displaystyle 8^{3}\div 2^{2}=$

Possible Answers:

$\displaystyle 23$

$\displaystyle 12$

128 $\displaystyle 128$

$\displaystyle 34$

Correct answer:

128 $\displaystyle 128$

Explanation:

First find the exponent value for each number:

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

Then divide accordingly. The answer is 128.

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

$\displaystyle 11+39=12+28+2a$

Possible Answers:

$\displaystyle 4$

$\displaystyle 20$

$\displaystyle 10$

2.5 $\displaystyle 2.5$

$\displaystyle 5$

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:

$\displaystyle 50-40=40+2a-40$

10=2a $\displaystyle 10=2a$

Finally, divide both sides by 2.

$10\div 2=2a\div 2$ $\displaystyle 10\div 2=2a\div 2$

The answer is 5=a $\displaystyle 5=a$

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Example Question #2 : Equations

$\displaystyle 13 + 27=12+3+ 5a$

Possible Answers:

$\displaystyle 3$

5.5 $\displaystyle 5.5$

$\displaystyle 6$

$\displaystyle 5$

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:

$\displaystyle 40-15=15+ 5a-15$

25=5a $\displaystyle 25=5a$

Finally, divide each side by 5:

$25\div 5=5a\div 5$ $\displaystyle 25\div 5=5a\div 5$

5=a $\displaystyle 5=a$

The answer is 5.

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Equations

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #1 : Equations

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

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

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

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

Example Question #1 : Equations

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

Example Question #1 : Equations

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

Example Question #2 : Equations

All ISEE Middle Level Math Resources

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