To figure out the value, translate the question into an equation, knowing that "is" means equals, and "of" means multiply:

\(\displaystyle \small 4 = 48\%*x\)

To solve, turn the percentage into a decimal:

\(\displaystyle \small 4=0.48*x\) now divide both sides by 0.48

\(\displaystyle \small 8.\overline{3}=x\)

To determine the whole, translate the question into an equation, knowing that "is" means equals and "of" means multiply:

\(\displaystyle \small 10 = 180\%*x\) convert the percentage into a decimal:

\(\displaystyle \small 10 = 1.8*x\) divide both sides by 1.8

\(\displaystyle \small 5.\overline{5}=x\)

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:

\(\displaystyle 80\% \div 100 = .80\)

\(\displaystyle .80 \div 250 = 312.5\)

Therefore, \(\displaystyle 250\) is \(\displaystyle 80\%\) of \(\displaystyle 312.5\)

If \(\displaystyle 33\%\) of the students in Mrs. Roger's 5th grade class received an "A" on the math test, and the number of students who received an "A" was \(\displaystyle 12\), how many students are there in Mrs. Roger's 5th grade class? Round to the nearest student.

This is question is asking us to find the whole from a percentage and a part. We know that \(\displaystyle 12\) students make up \(\displaystyle 33\%\) of the whole class. We need to find the total number of students in the class. The trickiest part of this is the setup.

We can start by thinking of it like so

\(\displaystyle 12=.33W\)

Meaning that \(\displaystyle 33\%\) of the whole (W) is equal to \(\displaystyle 12\) .

Then we use some basic rearranging to divide both sides by \(\displaystyle .33\)

\(\displaystyle W=\frac{12}{.33}=36.\bar{36}=36\: students\)

So there are \(\displaystyle 36\) students in the class.

Note, there cannot be \(\displaystyle 37\) students, because we must round down. \(\displaystyle .36\) is not \(\displaystyle .5\) or greater, so we cannot round up to \(\displaystyle 37\).

Since \(\displaystyle 28\) eggs account for \(\displaystyle 40\%\) of the total batch, we can determine the total number of eggs as such:

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

Dividing \(\displaystyle 15\%\) of the total earnings by \(\displaystyle 15\%\) will determine the total amount of money earned:

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

If Todd has already paid \(\displaystyle 45\%\) of his tuition, then he still owes \(\displaystyle 55\%\) of the total cost. \(\displaystyle \$4,500\) is \(\displaystyle 55\%\) of the total cost of tuition, which we can use to calculate the full cost:

\(\displaystyle \frac{100\%}{55\%}\cdot\$4,500=\$8,182\)

First of all, it should be understood that since \(\displaystyle 25\%\) of Oscar's annual earnings are taken, than \(\displaystyle 25\%\) of his monthly salary is also taken. By that reasoning, \(\displaystyle \$722.85\) is \(\displaystyle 25\%\) of Oscar's monthly salary, which we can then use to determine his annual earnings:

\(\displaystyle \frac{\$722.85}{1month} \cdot\frac{100\%}{25\%}=\frac{\$2,891.40}{1month}\)

\(\displaystyle \frac{\$2,891.40}{1 month}\cdot\frac{12 months}{1 year}=\frac{\$34696.80}{1year}\)

We can determine Charlie's monthly earnings given the amount he spends in rent and the percent of his income that it consumes:

\(\displaystyle \frac{\$6325}{1 month}\cdot\frac{100\%}{62\%}=\frac{\$10201.61}{month}\)

With this value we can now determine Charlie's annual income:

\(\displaystyle \frac{\$10201.61}{month}\cdot\frac{12 months}{1 year}=\frac{\$122419.35}{year}\)

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,

\(\displaystyle 0.3 \cdot x = 6\)

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

\(\displaystyle \frac{0.3 \cdot x}{0.3} = \frac{6}{0.3}\)

\(\displaystyle x = 20\)

Therefore, 30% of 20 is 6.