Equations - ISEE Middle Level Math

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Question

If , solve for .

Answer

First, subtract 3 from both sides:

$\dpi{100} 4x+3-3=15-3$

$\dpi{100} 4x=12$

Now divide by 4 on both sides:

$\dpi{100} \frac{4x}{4}=\frac{12}{4}$

$\dpi{100} x=3$

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Question

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

Answer

To solve:

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

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

Then, subtract 15 from each side of the equation.

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

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

$\small \small a=9$

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Question

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?

Answer

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

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Question

Solve for :

Answer

Subtract 19, then divide by 7:

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

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Question

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

Answer

First multiply the original price by 30%.

$120\ast .30=36$

Then subtract that amount from the original price.

The sale price is $84.00

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Question

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

Answer

First solve the parentheses.

$8 * 10 \div 4=$

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

$80\div 4=20$

The answer is 20.

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Question

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

Answer

First, convert each mixed number into an improper fraction.

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

Then, reduce where possible and multiply.

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

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

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Question

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

Answer

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

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

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

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Question

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

Answer

First find the exponent value for each number:

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

Then divide accordingly. The answer is 128.

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Question

Solve for the variable:

Answer

First, combine the integers on the left side of the equation, and then do the same on the right:

Then subtract 16 from each side:

8 = 4a

Finally, divide both sides by 4 to isolate the variable:

$8\div 4=4a\div 4$

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Question

Answer

First follow order of operations and solve on each side.

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

Finally, divide both sides by 2.

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

The answer is

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Question

Answer

First solve with order of operations on each side:

Then subtract 15 from each side:

Finally, divide each side by 5:

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

The answer is 5.

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Question

$7 \ast \left ( 3\ast 5 \right )\div \left ( 25\div 5 \right )=$

Answer

Solve inside the parentheses first:

$7 \ast (15) \div (5)=$

Follow order of operations to solve:

$105 \div 5=21$

The answer is 21.

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Question

Melissa is going on a road trip to her mother's house in another state. On a full tank of gas, she can travel 230 miles. At least how many times will she need to fill up her gas tank if her mother lives 950 miles away?

Answer

Divide the total distance (950) by the number of miles per full tank of gas (230).

$950\div 230=4.1$

Therefore, she will have to fill up her tank with gas at least 5 times.

Answer is at least 5 times.

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Question

$12a + 2a -18= 3(6) + 2(5\ast 2)$

Answer

First solve what is inside parentheses and follow the order of operations:

$12a + 2a -18= 3(6) + 2(5\ast 2)$

Then, add 18 to each side:

Finally, divide each side my 14:

$14a \div 14= 56\div 14$

The answer is 4.

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Question

$3\frac{3}{9} \div 5\frac{1}{5}=$

Answer

First, convert each fraction into an improper fraction.

$\frac{30}{9} \div \frac{26}{5}=$

Then, change the operation to multiplication and flip the second fraction.

$\frac{30}{9} \ast \frac{5}{26}=$

Reduce and multiply.

$\frac{30}{9}\ast \frac{5}{26}=\frac{10}{3}\ast \frac{5}{26}=\frac{5}{3}\ast \frac{5}{13}=\frac{25}{39}$

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Question

$7\frac{3}{6}\div 11\frac{2}{3}=$

Answer

First, convert each mixed number into an improper fraction:

$\frac{45}{6}\div \frac{35}{3}=$

Then, change the operation to multiplication and flip the second fraction:

$\frac{45}{6}\ast \frac{3}{35}=$

Reduce and multiply:

$\frac{45}{6}\ast \frac{3}{35}=\frac{9}{2}\ast \frac{1}{7}=\frac{9}{14}$

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Question

Jasmine is participating in a swimming race. If the race is 3000 yards, what percentage of the race has she completed at the 2400 yardline?

Answer

Divide $2400\div 3000=.80$ .

Answer: Jasmine has completed 80% of the race.

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Question

Nelson received $64.00 in holiday gifts. If he would like to buy a baseball bat for $16.00, a glove for $34.00, and a cap for $11.00, how much money will he have left over?

Answer

First, add up all the items on his wish list:

Then, subtract that amount from the original amount:

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Question

$14\frac{2}{7}\div 2\frac{4}{14}=$

Answer

First, convert each fraction into an improper fraction. Then, change the operation to multiplication and flip the second fraction. Reduce and multiply.

$14\frac{2}{7}\div 2\frac{4}{14}=\frac{100}{7}\div \frac{32}{14}=\frac{100}{7}\cdot \frac{14}{32}=\frac{25}{1}\cdot \frac{2}{8}=\frac{50}{8}=\frac{25}{4}=6\frac{1}{4}$

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