Algebra - How to find the whole from the part with percentage

What number of is nine?

$\frac{1}{9}$

$\frac{1}{90}$

Explanation

Let the number be .

Some number of ten percent means some number multiplied by ten percent.

A percentage is a number out of 100 parts.

Set up the equation.

$x(\frac{10}{100}) = 9$

Reduce the fraction and simplify the left side.

$x(\frac{1}{10}) = 9$

Multiply both sides by ten to eliminate the fraction.

$x(\frac{1}{10}) \times 10= 9\times 10$

Simplify both sides.

The answer is .

is of what number?

Explanation

To find the whole from the part given a percentage, we divide our known part by the decimal equivalent of the percentage, which we find by dividing the percentage by one-hundred:

$80% \div 100 = .80$

$.80 \div 250 = 312.5$

Therefore, is of

30% of what number is 6?

Explanation

When we don't know the value of a number, we assign it a variable. In this case,

30% of what number is 6

can be written as

30% of x is 6

Now, we will write 30% as a decimal. We get

0.3 of x is 6

We know when we see "is" that means equals. So,

0.3 of x = 6

We also know when we are finding percentages of numbers, we multiply. So,

$0.3 \cdot x = 6$

Now, we solve for x. We divide both sides by 0.3. We get

$\frac{0.3 \cdot x}{0.3} = \frac{6}{0.3}$

Therefore, 30% of 20 is 6.

What number of five percent is ten?

Explanation

Set up the equation so that some number multiplied with five percent is equal to ten.

$x \cdot 5%=10$

The percentage can be rewritten as a fraction.

$x \cdot \frac{5}{100}=10$

Simplify the fraction.

$x \cdot \frac{1}{20}=10$

Multiply by the denominator on both sides to eliminate the fraction.

$x \cdot \frac{1}{20}\cdot20=10\cdot20$

Simplify both sides.

The answer is:

70% of a quantity is 35. What is the quantity?

Explanation

We can write this as an equation:

$0.70\cdot x=35$

$x=\frac{35}{0.7}$

Nine is fifty percent of what number?

Explanation

Set up an equation such that a number times 50 out of 100 parts is nine.

$x \cdot \frac{50}{100}=9$

Solve this equation.

$x \cdot \frac{1}{2}=9$

Multply by two on both sides to eliminate the fraction.

$x \cdot \frac{1}{2} \times 2=9 \times2$

Simplify both sides.

of the eggs gathered in the hen house were brown and there were of them. How many eggs in total were gathered?

Explanation

Since eggs account for of the total batch, we can determine the total number of eggs as such:

$28,eggs\cdot\frac{100%}{40%}=28,eggs\cdot2.5=70,eggs$

If 45 is 15% of , find the value of .

Explanation

The key to this problem is identifying that "15% of " is the same as . With this information, we can write out the simple equation

Dividing both sides by gives us

For helping run the snack bar Rodney was paid of total earnings for the day. If Rodney was paid , what was the total earnings for the snack bar?

Explanation

Dividing of the total earnings by will determine the total amount of money earned:

$$37.50\cdot\frac{100%}{15%}=$37.50\cdot6.67=$250$

Dana spent 24% of her savings on a laptop that costs $900. How much savings does she have left?

Explanation

We know that prior to her purchase, $900 was 24% of Dana's Savings. Therefore, Dana's total savings prior to her purchase can be modeled as , where is Dana's total savings. Solving for would give you , which indicates that Dana's savings was $3750 prior to her purchase. After her purchase, she will have $2850 left.

How to find the whole from the part with percentage

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